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allein ",[568,1932,1933],{},"nicht",", die Quotienten müssen von ",[578,1936,1938,1951],{"className":1937},[581],[578,1939,1941],{"className":1940},[585],[587,1942,1943],{"xmlns":589},[591,1944,1945,1949],{},[594,1946,1947],{},[605,1948,607],{},[609,1950,607],{"encoding":611},[578,1952,1954],{"className":1953,"ariaHidden":617},[616],[578,1955,1957,1960],{"className":1956},[621],[578,1958],{"className":1959,"style":650},[625],[578,1961,607],{"className":1962},[630]," weg beschränkt bleiben. Gleichwertig formuliert man mit dem Limes superior ",[578,1965,1967,2015],{"className":1966},[581],[578,1968,1970],{"className":1969},[585],[587,1971,1972],{"xmlns":589},[591,1973,1974,2012],{},[594,1975,1976,1979,1982,2008,2010],{},[597,1977,1978],{"mathvariant":733},"lim sup",[601,1980,1981],{},"⁡",[594,1983,1984,1986,2006],{},[601,1985,899],{"fence":617},[901,1987,1988,2000],{},[904,1989,1990,1992],{},[597,1991,908],{},[594,1993,1994,1996,1998],{},[597,1995,913],{},[601,1997,916],{},[605,1999,607],{},[904,2001,2002,2004],{},[597,2003,908],{},[597,2005,913],{},[601,2007,899],{"fence":617},[601,2009,603],{},[605,2011,607],{},[609,2013,2014],{"encoding":611},"\\limsup \\left|\\frac{a_{n+1}}{a_n}\\right| \u003C 1",[578,2016,2018,2281],{"className":2017,"ariaHidden":617},[616],[578,2019,2021,2024,2041,2044,2272,2275,2278],{"className":2020},[621],[578,2022],{"className":2023,"style":944},[625],[578,2025,2028,2033,2037],{"className":2026},[2027],"mop",[578,2029,2032],{"className":2030},[630,2031],"mathrm","lim",[578,2034],{"className":2035,"style":2036},[635],"margin-right:0.1667em;",[578,2038,2040],{"className":2039},[630,2031],"sup",[578,2042],{"className":2043,"style":2036},[635],[578,2045,2047,2084,2235],{"className":2046},[948],[578,2048,2050],{"className":2049},[952],[578,2051,2053],{"className":2052},[956,957],[578,2054,2056,2076],{"className":2055},[961,962],[578,2057,2059,2073],{"className":2058},[966],[578,2060,2062],{"className":2061,"style":971},[970],[578,2063,2064,2067],{"style":974},[578,2065],{"className":2066,"style":979},[978],[578,2068,2069],{"style":982},[984,2070,2071],{"xmlns":986,"width":987,"height":988,"viewBox":989},[991,2072],{"d":993},[578,2074,998],{"className":2075},[997],[578,2077,2079],{"className":2078},[966],[578,2080,2082],{"className":2081,"style":1005},[970],[578,2083],{},[578,2085,2087,2090,2232],{"className":2086},[630],[578,2088],{"className":2089},[952,1014],[578,2091,2093],{"className":2092},[901],[578,2094,2096,2224],{"className":2095},[961,962],[578,2097,2099,2221],{"className":2098},[966],[578,2100,2102,2153,2161],{"className":2101,"style":1027},[970],[578,2103,2104,2107],{"style":1030},[578,2105],{"className":2106,"style":1034},[978],[578,2108,2110],{"className":2109},[1038,1039,1040,1041],[578,2111,2113],{"className":2112},[630,1041],[578,2114,2116,2119],{"className":2115},[630,1041],[578,2117,908],{"className":2118},[630,631,1041],[578,2120,2122],{"className":2121},[1054],[578,2123,2125,2145],{"className":2124},[961,962],[578,2126,2128,2142],{"className":2127},[966],[578,2129,2131],{"className":2130,"style":1064},[970],[578,2132,2133,2136],{"style":1067},[578,2134],{"className":2135,"style":1071},[978],[578,2137,2139],{"className":2138},[1038,1075,1076,1041],[578,2140,913],{"className":2141},[630,631,1041],[578,2143,998],{"className":2144},[997],[578,2146,2148],{"className":2147},[966],[578,2149,2151],{"className":2150,"style":1089},[970],[578,2152],{},[578,2154,2155,2158],{"style":1094},[578,2156],{"className":2157,"style":1034},[978],[578,2159],{"className":2160,"style":1102},[1101],[578,2162,2163,2166],{"style":1105},[578,2164],{"className":2165,"style":1034},[978],[578,2167,2169],{"className":2168},[1038,1039,1040,1041],[578,2170,2172],{"className":2171},[630,1041],[578,2173,2175,2178],{"className":2174},[630,1041],[578,2176,908],{"className":2177},[630,631,1041],[578,2179,2181],{"className":2180},[1054],[578,2182,2184,2213],{"className":2183},[961,962],[578,2185,2187,2210],{"className":2186},[966],[578,2188,2190],{"className":2189,"style":1133},[970],[578,2191,2192,2195],{"style":1067},[578,2193],{"className":2194,"style":1071},[978],[578,2196,2198],{"className":2197},[1038,1075,1076,1041],[578,2199,2201,2204,2207],{"className":2200},[630,1041],[578,2202,913],{"className":2203},[630,631,1041],[578,2205,916],{"className":2206},[1151,1041],[578,2208,607],{"className":2209},[630,1041],[578,2211,998],{"className":2212},[997],[578,2214,2216],{"className":2215},[966],[578,2217,2219],{"className":2218,"style":1164},[970],[578,2220],{},[578,2222,998],{"className":2223},[997],[578,2225,2227],{"className":2226},[966],[578,2228,2230],{"className":2229,"style":1176},[970],[578,2231],{},[578,2233],{"className":2234},[1182,1014],[578,2236,2238],{"className":2237},[1182],[578,2239,2241],{"className":2240},[956,957],[578,2242,2244,2264],{"className":2243},[961,962],[578,2245,2247,2261],{"className":2246},[966],[578,2248,2250],{"className":2249,"style":971},[970],[578,2251,2252,2255],{"style":974},[578,2253],{"className":2254,"style":979},[978],[578,2256,2257],{"style":982},[984,2258,2259],{"xmlns":986,"width":987,"height":988,"viewBox":989},[991,2260],{"d":993},[578,2262,998],{"className":2263},[997],[578,2265,2267],{"className":2266},[966],[578,2268,2270],{"className":2269,"style":1005},[970],[578,2271],{},[578,2273],{"className":2274,"style":636},[635],[578,2276,603],{"className":2277},[640],[578,2279],{"className":2280,"style":636},[635],[578,2282,2284,2287],{"className":2283},[621],[578,2285],{"className":2286,"style":650},[625],[578,2288,607],{"className":2289},[630],".",[564,2292,2293,2294,2358],{},"Das Kriterium eignet sich besonders für Glieder mit Fakultäten und Potenzen ",[578,2295,2297,2317],{"className":2296},[581],[578,2298,2300],{"className":2299},[585],[587,2301,2302],{"xmlns":589},[591,2303,2304,2314],{},[594,2305,2306],{},[2307,2308,2309,2312],"msup",{},[597,2310,2311],{},"c",[597,2313,913],{},[609,2315,2316],{"encoding":611},"c^n",[578,2318,2320],{"className":2319,"ariaHidden":617},[616],[578,2321,2323,2327],{"className":2322},[621],[578,2324],{"className":2325,"style":2326},[625],"height:0.6644em;",[578,2328,2330,2333],{"className":2329},[630],[578,2331,2311],{"className":2332},[630,631],[578,2334,2336],{"className":2335},[1054],[578,2337,2339],{"className":2338},[961],[578,2340,2342],{"className":2341},[966],[578,2343,2345],{"className":2344,"style":2326},[970],[578,2346,2348,2352],{"style":2347},"top:-3.063em;margin-right:0.05em;",[578,2349],{"className":2350,"style":2351},[978],"height:2.7em;",[578,2353,2355],{"className":2354},[1038,1039,1040,1041],[578,2356,913],{"className":2357},[630,631,1041],", weil sich diese im Quotienten stark kürzen. Es ist das übliche Werkzeug, um den Konvergenzradius einer Potenzreihe zu bestimmen.",[559,2360,2362],{"id":2361},"beispiele","Beispiele",[564,2364,2365,2512],{},[578,2366,2368,2394],{"className":2367},[581],[578,2369,2371],{"className":2370},[585],[587,2372,2373],{"xmlns":589},[591,2374,2375,2391],{},[594,2376,2377,2380],{},[601,2378,2379],{},"∑",[901,2381,2382,2384],{},[597,2383,913],{},[2307,2385,2386,2389],{},[605,2387,2388],{},"2",[597,2390,913],{},[609,2392,2393],{"encoding":611},"\\sum \\frac{n}{2^n}",[578,2395,2397],{"className":2396,"ariaHidden":617},[616],[578,2398,2400,2404,2410,2413],{"className":2399},[621],[578,2401],{"className":2402,"style":2403},[625],"height:1.095em;vertical-align:-0.345em;",[578,2405,2379],{"className":2406,"style":2409},[2027,2407,2408],"op-symbol","small-op","position:relative;top:0em;",[578,2411],{"className":2412,"style":2036},[635],[578,2414,2416,2419,2509],{"className":2415},[630],[578,2417],{"className":2418},[952,1014],[578,2420,2422],{"className":2421},[901],[578,2423,2425,2500],{"className":2424},[961,962],[578,2426,2428,2497],{"className":2427},[966],[578,2429,2432,2474,2482],{"className":2430,"style":2431},[970],"height:0.6954em;",[578,2433,2434,2437],{"style":1030},[578,2435],{"className":2436,"style":1034},[978],[578,2438,2440],{"className":2439},[1038,1039,1040,1041],[578,2441,2443],{"className":2442},[630,1041],[578,2444,2446,2449],{"className":2445},[630,1041],[578,2447,2388],{"className":2448},[630,1041],[578,2450,2452],{"className":2451},[1054],[578,2453,2455],{"className":2454},[961],[578,2456,2458],{"className":2457},[966],[578,2459,2462],{"className":2460,"style":2461},[970],"height:0.5935em;",[578,2463,2465,2468],{"style":2464},"top:-2.786em;margin-right:0.0714em;",[578,2466],{"className":2467,"style":1071},[978],[578,2469,2471],{"className":2470},[1038,1075,1076,1041],[578,2472,913],{"className":2473},[630,631,1041],[578,2475,2476,2479],{"style":1094},[578,2477],{"className":2478,"style":1034},[978],[578,2480],{"className":2481,"style":1102},[1101],[578,2483,2485,2488],{"style":2484},"top:-3.394em;",[578,2486],{"className":2487,"style":1034},[978],[578,2489,2491],{"className":2490},[1038,1039,1040,1041],[578,2492,2494],{"className":2493},[630,1041],[578,2495,913],{"className":2496},[630,631,1041],[578,2498,998],{"className":2499},[997],[578,2501,2503],{"className":2502},[966],[578,2504,2507],{"className":2505,"style":2506},[970],"height:0.345em;",[578,2508],{},[578,2510],{"className":2511},[1182,1014],": Der Quotient ist",[578,2514,2517],{"className":2515},[2516],"katex-display",[578,2518,2520,2608],{"className":2519},[581],[578,2521,2523],{"className":2522},[585],[587,2524,2526],{"xmlns":589,"display":2525},"block",[591,2527,2528,2605],{},[594,2529,2530,2574,2576,2592,2595,2601,2603],{},[901,2531,2532,2562],{},[594,2533,2534,2538,2540,2542,2544,2547,2550],{},[601,2535,2537],{"stretchy":2536},"false","(",[597,2539,913],{},[601,2541,916],{},[605,2543,607],{},[601,2545,2546],{"stretchy":2536},")",[597,2548,2549],{"mathvariant":733},"\u002F",[2307,2551,2552,2554],{},[605,2553,2388],{},[594,2555,2556,2558,2560],{},[597,2557,913],{},[601,2559,916],{},[605,2561,607],{},[594,2563,2564,2566,2568],{},[597,2565,913],{},[597,2567,2549],{"mathvariant":733},[2307,2569,2570,2572],{},[605,2571,2388],{},[597,2573,913],{},[601,2575,730],{},[901,2577,2578,2586],{},[594,2579,2580,2582,2584],{},[597,2581,913],{},[601,2583,916],{},[605,2585,607],{},[594,2587,2588,2590],{},[605,2589,2388],{},[597,2591,913],{},[601,2593,2594],{},"→",[901,2596,2597,2599],{},[605,2598,607],{},[605,2600,2388],{},[601,2602,603],{},[605,2604,607],{},[609,2606,2607],{"encoding":611},"\\frac{(n + 1) \u002F 2^{n+1}}{n \u002F 2^n} = \\frac{n + 1}{2n} \\to \\frac{1}{2} \u003C 1",[578,2609,2611,2788,2883,2960],{"className":2610,"ariaHidden":617},[616],[578,2612,2614,2618,2779,2782,2785],{"className":2613},[621],[578,2615],{"className":2616,"style":2617},[625],"height:2.4271em;vertical-align:-0.936em;",[578,2619,2621,2624,2776],{"className":2620},[630],[578,2622],{"className":2623},[952,1014],[578,2625,2627],{"className":2626},[901],[578,2628,2630,2767],{"className":2629},[961,962],[578,2631,2633,2764],{"className":2632},[966],[578,2634,2637,2683,2691],{"className":2635,"style":2636},[970],"height:1.4911em;",[578,2638,2640,2643],{"style":2639},"top:-2.314em;",[578,2641],{"className":2642,"style":1034},[978],[578,2644,2646,2649,2652],{"className":2645},[630],[578,2647,913],{"className":2648},[630,631],[578,2650,2549],{"className":2651},[630],[578,2653,2655,2658],{"className":2654},[630],[578,2656,2388],{"className":2657},[630],[578,2659,2661],{"className":2660},[1054],[578,2662,2664],{"className":2663},[961],[578,2665,2667],{"className":2666},[966],[578,2668,2671],{"className":2669,"style":2670},[970],"height:0.5904em;",[578,2672,2674,2677],{"style":2673},"top:-2.989em;margin-right:0.05em;",[578,2675],{"className":2676,"style":2351},[978],[578,2678,2680],{"className":2679},[1038,1039,1040,1041],[578,2681,913],{"className":2682},[630,631,1041],[578,2684,2685,2688],{"style":1094},[578,2686],{"className":2687,"style":1034},[978],[578,2689],{"className":2690,"style":1102},[1101],[578,2692,2694,2697],{"style":2693},"top:-3.677em;",[578,2695],{"className":2696,"style":1034},[978],[578,2698,2700,2703,2706,2710,2713,2716,2719,2722,2725],{"className":2699},[630],[578,2701,2537],{"className":2702},[952],[578,2704,913],{"className":2705},[630,631],[578,2707],{"className":2708,"style":2709},[635],"margin-right:0.2222em;",[578,2711,916],{"className":2712},[1151],[578,2714],{"className":2715,"style":2709},[635],[578,2717,607],{"className":2718},[630],[578,2720,2546],{"className":2721},[1182],[578,2723,2549],{"className":2724},[630],[578,2726,2728,2731],{"className":2727},[630],[578,2729,2388],{"className":2730},[630],[578,2732,2734],{"className":2733},[1054],[578,2735,2737],{"className":2736},[961],[578,2738,2740],{"className":2739},[966],[578,2741,2744],{"className":2742,"style":2743},[970],"height:0.8141em;",[578,2745,2746,2749],{"style":2347},[578,2747],{"className":2748,"style":2351},[978],[578,2750,2752],{"className":2751},[1038,1039,1040,1041],[578,2753,2755,2758,2761],{"className":2754},[630,1041],[578,2756,913],{"className":2757},[630,631,1041],[578,2759,916],{"className":2760},[1151,1041],[578,2762,607],{"className":2763},[630,1041],[578,2765,998],{"className":2766},[997],[578,2768,2770],{"className":2769},[966],[578,2771,2774],{"className":2772,"style":2773},[970],"height:0.936em;",[578,2775],{},[578,2777],{"className":2778},[1182,1014],[578,2780],{"className":2781,"style":636},[635],[578,2783,730],{"className":2784},[640],[578,2786],{"className":2787,"style":636},[635],[578,2789,2791,2795,2874,2877,2880],{"className":2790},[621],[578,2792],{"className":2793,"style":2794},[625],"height:2.0074em;vertical-align:-0.686em;",[578,2796,2798,2801,2871],{"className":2797},[630],[578,2799],{"className":2800},[952,1014],[578,2802,2804],{"className":2803},[901],[578,2805,2807,2862],{"className":2806},[961,962],[578,2808,2810,2859],{"className":2809},[966],[578,2811,2814,2828,2836],{"className":2812,"style":2813},[970],"height:1.3214em;",[578,2815,2816,2819],{"style":2639},[578,2817],{"className":2818,"style":1034},[978],[578,2820,2822,2825],{"className":2821},[630],[578,2823,2388],{"className":2824},[630],[578,2826,913],{"className":2827},[630,631],[578,2829,2830,2833],{"style":1094},[578,2831],{"className":2832,"style":1034},[978],[578,2834],{"className":2835,"style":1102},[1101],[578,2837,2838,2841],{"style":2693},[578,2839],{"className":2840,"style":1034},[978],[578,2842,2844,2847,2850,2853,2856],{"className":2843},[630],[578,2845,913],{"className":2846},[630,631],[578,2848],{"className":2849,"style":2709},[635],[578,2851,916],{"className":2852},[1151],[578,2854],{"className":2855,"style":2709},[635],[578,2857,607],{"className":2858},[630],[578,2860,998],{"className":2861},[997],[578,2863,2865],{"className":2864},[966],[578,2866,2869],{"className":2867,"style":2868},[970],"height:0.686em;",[578,2870],{},[578,2872],{"className":2873},[1182,1014],[578,2875],{"className":2876,"style":636},[635],[578,2878,2594],{"className":2879},[640],[578,2881],{"className":2882,"style":636},[635],[578,2884,2886,2889,2951,2954,2957],{"className":2885},[621],[578,2887],{"className":2888,"style":2794},[625],[578,2890,2892,2895,2948],{"className":2891},[630],[578,2893],{"className":2894},[952,1014],[578,2896,2898],{"className":2897},[901],[578,2899,2901,2940],{"className":2900},[961,962],[578,2902,2904,2937],{"className":2903},[966],[578,2905,2907,2918,2926],{"className":2906,"style":2813},[970],[578,2908,2909,2912],{"style":2639},[578,2910],{"className":2911,"style":1034},[978],[578,2913,2915],{"className":2914},[630],[578,2916,2388],{"className":2917},[630],[578,2919,2920,2923],{"style":1094},[578,2921],{"className":2922,"style":1034},[978],[578,2924],{"className":2925,"style":1102},[1101],[578,2927,2928,2931],{"style":2693},[578,2929],{"className":2930,"style":1034},[978],[578,2932,2934],{"className":2933},[630],[578,2935,607],{"className":2936},[630],[578,2938,998],{"className":2939},[997],[578,2941,2943],{"className":2942},[966],[578,2944,2946],{"className":2945,"style":2868},[970],[578,2947],{},[578,2949],{"className":2950},[1182,1014],[578,2952],{"className":2953,"style":636},[635],[578,2955,603],{"className":2956},[640],[578,2958],{"className":2959,"style":636},[635],[578,2961,2963,2966],{"className":2962},[621],[578,2964],{"className":2965,"style":650},[625],[578,2967,607],{"className":2968},[630],[564,2970,2971,2972,3000,3001,3053,3054,2290],{},"Die Reihe konvergiert (ihr Wert ist ",[578,2973,2975,2988],{"className":2974},[581],[578,2976,2978],{"className":2977},[585],[587,2979,2980],{"xmlns":589},[591,2981,2982,2986],{},[594,2983,2984],{},[605,2985,2388],{},[609,2987,2388],{"encoding":611},[578,2989,2991],{"className":2990,"ariaHidden":617},[616],[578,2992,2994,2997],{"className":2993},[621],[578,2995],{"className":2996,"style":650},[625],[578,2998,2388],{"className":2999},[630],"). Für ",[578,3002,3004,3023],{"className":3003},[581],[578,3005,3007],{"className":3006},[585],[587,3008,3009],{"xmlns":589},[591,3010,3011,3020],{},[594,3012,3013,3015,3017],{},[597,3014,913],{},[601,3016,730],{},[605,3018,3019],{},"1000",[609,3021,3022],{"encoding":611},"n = 1000",[578,3024,3026,3044],{"className":3025,"ariaHidden":617},[616],[578,3027,3029,3032,3035,3038,3041],{"className":3028},[621],[578,3030],{"className":3031,"style":766},[625],[578,3033,913],{"className":3034},[630,631],[578,3036],{"className":3037,"style":636},[635],[578,3039,730],{"className":3040},[640],[578,3042],{"className":3043,"style":636},[635],[578,3045,3047,3050],{"className":3046},[621],[578,3048],{"className":3049,"style":650},[625],[578,3051,3019],{"className":3052},[630]," ist der Quotient schon ",[578,3055,3057,3072],{"className":3056},[581],[578,3058,3060],{"className":3059},[585],[587,3061,3062],{"xmlns":589},[591,3063,3064,3069],{},[594,3065,3066],{},[605,3067,3068],{},"0,5005",[609,3070,3071],{"encoding":611},"0{,}5005",[578,3073,3075],{"className":3074,"ariaHidden":617},[616],[578,3076,3078,3082,3086,3094],{"className":3077},[621],[578,3079],{"className":3080,"style":3081},[625],"height:0.8389em;vertical-align:-0.1944em;",[578,3083,3085],{"className":3084},[630],"0",[578,3087,3089],{"className":3088},[630],[578,3090,3093],{"className":3091},[3092],"mpunct",",",[578,3095,3097],{"className":3096},[630],"5005",[564,3099,3100,3248,3249,3362,3363,3391,3392,2290],{},[578,3101,3103,3132],{"className":3102},[581],[578,3104,3106],{"className":3105},[585],[587,3107,3108],{"xmlns":589},[591,3109,3110,3129],{},[594,3111,3112,3114],{},[601,3113,2379],{},[901,3115,3116,3122],{},[2307,3117,3118,3120],{},[605,3119,2388],{},[597,3121,913],{},[594,3123,3124,3126],{},[597,3125,913],{},[601,3127,3128],{"stretchy":2536},"!",[609,3130,3131],{"encoding":611},"\\sum \\frac{2^n}{n!}",[578,3133,3135],{"className":3134,"ariaHidden":617},[616],[578,3136,3138,3142,3145,3148],{"className":3137},[621],[578,3139],{"className":3140,"style":3141},[625],"height:1.256em;vertical-align:-0.345em;",[578,3143,2379],{"className":3144,"style":2409},[2027,2407,2408],[578,3146],{"className":3147,"style":2036},[635],[578,3149,3151,3154,3245],{"className":3150},[630],[578,3152],{"className":3153},[952,1014],[578,3155,3157],{"className":3156},[901],[578,3158,3160,3237],{"className":3159},[961,962],[578,3161,3163,3234],{"className":3162},[966],[578,3164,3167,3184,3192],{"className":3165,"style":3166},[970],"height:0.911em;",[578,3168,3169,3172],{"style":1030},[578,3170],{"className":3171,"style":1034},[978],[578,3173,3175],{"className":3174},[1038,1039,1040,1041],[578,3176,3178,3181],{"className":3177},[630,1041],[578,3179,913],{"className":3180},[630,631,1041],[578,3182,3128],{"className":3183},[1182,1041],[578,3185,3186,3189],{"style":1094},[578,3187],{"className":3188,"style":1034},[978],[578,3190],{"className":3191,"style":1102},[1101],[578,3193,3194,3197],{"style":2484},[578,3195],{"className":3196,"style":1034},[978],[578,3198,3200],{"className":3199},[1038,1039,1040,1041],[578,3201,3203],{"className":3202},[630,1041],[578,3204,3206,3209],{"className":3205},[630,1041],[578,3207,2388],{"className":3208},[630,1041],[578,3210,3212],{"className":3211},[1054],[578,3213,3215],{"className":3214},[961],[578,3216,3218],{"className":3217},[966],[578,3219,3222],{"className":3220,"style":3221},[970],"height:0.7385em;",[578,3223,3225,3228],{"style":3224},"top:-2.931em;margin-right:0.0714em;",[578,3226],{"className":3227,"style":1071},[978],[578,3229,3231],{"className":3230},[1038,1075,1076,1041],[578,3232,913],{"className":3233},[630,631,1041],[578,3235,998],{"className":3236},[997],[578,3238,3240],{"className":3239},[966],[578,3241,3243],{"className":3242,"style":2506},[970],[578,3244],{},[578,3246],{"className":3247},[1182,1014],": Der Quotient ",[578,3250,3252,3276],{"className":3251},[581],[578,3253,3255],{"className":3254},[585],[587,3256,3257],{"xmlns":589},[591,3258,3259,3273],{},[594,3260,3261],{},[901,3262,3263,3265],{},[605,3264,2388],{},[594,3266,3267,3269,3271],{},[597,3268,913],{},[601,3270,916],{},[605,3272,607],{},[609,3274,3275],{"encoding":611},"\\frac{2}{n + 1}",[578,3277,3279],{"className":3278,"ariaHidden":617},[616],[578,3280,3282,3286],{"className":3281},[621],[578,3283],{"className":3284,"style":3285},[625],"height:1.2484em;vertical-align:-0.4033em;",[578,3287,3289,3292,3359],{"className":3288},[630],[578,3290],{"className":3291},[952,1014],[578,3293,3295],{"className":3294},[901],[578,3296,3298,3350],{"className":3297},[961,962],[578,3299,3301,3347],{"className":3300},[966],[578,3302,3305,3325,3333],{"className":3303,"style":3304},[970],"height:0.8451em;",[578,3306,3307,3310],{"style":1030},[578,3308],{"className":3309,"style":1034},[978],[578,3311,3313],{"className":3312},[1038,1039,1040,1041],[578,3314,3316,3319,3322],{"className":3315},[630,1041],[578,3317,913],{"className":3318},[630,631,1041],[578,3320,916],{"className":3321},[1151,1041],[578,3323,607],{"className":3324},[630,1041],[578,3326,3327,3330],{"style":1094},[578,3328],{"className":3329,"style":1034},[978],[578,3331],{"className":3332,"style":1102},[1101],[578,3334,3335,3338],{"style":2484},[578,3336],{"className":3337,"style":1034},[978],[578,3339,3341],{"className":3340},[1038,1039,1040,1041],[578,3342,3344],{"className":3343},[630,1041],[578,3345,2388],{"className":3346},[630,1041],[578,3348,998],{"className":3349},[997],[578,3351,3353],{"className":3352},[966],[578,3354,3357],{"className":3355,"style":3356},[970],"height:0.4033em;",[578,3358],{},[578,3360],{"className":3361},[1182,1014]," geht gegen ",[578,3364,3366,3379],{"className":3365},[581],[578,3367,3369],{"className":3368},[585],[587,3370,3371],{"xmlns":589},[591,3372,3373,3377],{},[594,3374,3375],{},[605,3376,3085],{},[609,3378,3085],{"encoding":611},[578,3380,3382],{"className":3381,"ariaHidden":617},[616],[578,3383,3385,3388],{"className":3384},[621],[578,3386],{"className":3387,"style":650},[625],[578,3389,3085],{"className":3390},[630],", die Reihe konvergiert. Ihr Wert ist ",[578,3393,3395,3419],{"className":3394},[581],[578,3396,3398],{"className":3397},[585],[587,3399,3400],{"xmlns":589},[591,3401,3402,3416],{},[594,3403,3404,3411,3414],{},[2307,3405,3406,3409],{},[597,3407,3408],{},"e",[605,3410,2388],{},[601,3412,3413],{},"−",[605,3415,607],{},[609,3417,3418],{"encoding":611},"e^2 - 1",[578,3420,3422,3467],{"className":3421,"ariaHidden":617},[616],[578,3423,3425,3429,3458,3461,3464],{"className":3424},[621],[578,3426],{"className":3427,"style":3428},[625],"height:0.8974em;vertical-align:-0.0833em;",[578,3430,3432,3435],{"className":3431},[630],[578,3433,3408],{"className":3434},[630,631],[578,3436,3438],{"className":3437},[1054],[578,3439,3441],{"className":3440},[961],[578,3442,3444],{"className":3443},[966],[578,3445,3447],{"className":3446,"style":2743},[970],[578,3448,3449,3452],{"style":2347},[578,3450],{"className":3451,"style":2351},[978],[578,3453,3455],{"className":3454},[1038,1039,1040,1041],[578,3456,2388],{"className":3457},[630,1041],[578,3459],{"className":3460,"style":2709},[635],[578,3462,3413],{"className":3463},[1151],[578,3465],{"className":3466,"style":2709},[635],[578,3468,3470,3473],{"className":3469},[621],[578,3471],{"className":3472,"style":650},[625],[578,3474,607],{"className":3475},[630],[564,3477,3478,3623],{},[578,3479,3481,3509],{"className":3480},[581],[578,3482,3484],{"className":3483},[585],[587,3485,3486],{"xmlns":589},[591,3487,3488,3506],{},[594,3489,3490,3492],{},[601,3491,2379],{},[901,3493,3494,3500],{},[594,3495,3496,3498],{},[597,3497,913],{},[601,3499,3128],{"stretchy":2536},[2307,3501,3502,3504],{},[597,3503,913],{},[597,3505,913],{},[609,3507,3508],{"encoding":611},"\\sum \\frac{n!}{n^n}",[578,3510,3512],{"className":3511,"ariaHidden":617},[616],[578,3513,3515,3519,3522,3525],{"className":3514},[621],[578,3516],{"className":3517,"style":3518},[625],"height:1.2251em;vertical-align:-0.345em;",[578,3520,2379],{"className":3521,"style":2409},[2027,2407,2408],[578,3523],{"className":3524,"style":2036},[635],[578,3526,3528,3531,3620],{"className":3527},[630],[578,3529],{"className":3530},[952,1014],[578,3532,3534],{"className":3533},[901],[578,3535,3537,3612],{"className":3536},[961,962],[578,3538,3540,3609],{"className":3539},[966],[578,3541,3544,3584,3592],{"className":3542,"style":3543},[970],"height:0.8801em;",[578,3545,3546,3549],{"style":1030},[578,3547],{"className":3548,"style":1034},[978],[578,3550,3552],{"className":3551},[1038,1039,1040,1041],[578,3553,3555],{"className":3554},[630,1041],[578,3556,3558,3561],{"className":3557},[630,1041],[578,3559,913],{"className":3560},[630,631,1041],[578,3562,3564],{"className":3563},[1054],[578,3565,3567],{"className":3566},[961],[578,3568,3570],{"className":3569},[966],[578,3571,3573],{"className":3572,"style":2461},[970],[578,3574,3575,3578],{"style":2464},[578,3576],{"className":3577,"style":1071},[978],[578,3579,3581],{"className":3580},[1038,1075,1076,1041],[578,3582,913],{"className":3583},[630,631,1041],[578,3585,3586,3589],{"style":1094},[578,3587],{"className":3588,"style":1034},[978],[578,3590],{"className":3591,"style":1102},[1101],[578,3593,3594,3597],{"style":2484},[578,3595],{"className":3596,"style":1034},[978],[578,3598,3600],{"className":3599},[1038,1039,1040,1041],[578,3601,3603,3606],{"className":3602},[630,1041],[578,3604,913],{"className":3605},[630,631,1041],[578,3607,3128],{"className":3608},[1182,1041],[578,3610,998],{"className":3611},[997],[578,3613,3615],{"className":3614},[966],[578,3616,3618],{"className":3617,"style":2506},[970],[578,3619],{},[578,3621],{"className":3622},[1182,1014],": Nach Kürzen bleibt",[578,3625,3627],{"className":3626},[2516],[578,3628,3630,3740],{"className":3629},[581],[578,3631,3633],{"className":3632},[585],[587,3634,3635],{"xmlns":589,"display":2525},[591,3636,3637,3737],{},[594,3638,3639,3701,3703,3725,3727,3733,3735],{},[901,3640,3641,3683],{},[594,3642,3643,3645,3647,3649,3651,3653,3655,3659,3661,3663,3665,3667,3669,3671],{},[601,3644,2537],{"stretchy":2536},[597,3646,913],{},[601,3648,916],{},[605,3650,607],{},[601,3652,2546],{"stretchy":2536},[601,3654,3128],{"stretchy":2536},[3656,3657,3658],"mtext",{}," ",[597,3660,2549],{"mathvariant":733},[3656,3662,3658],{},[601,3664,2537],{"stretchy":2536},[597,3666,913],{},[601,3668,916],{},[605,3670,607],{},[2307,3672,3673,3675],{},[601,3674,2546],{"stretchy":2536},[594,3676,3677,3679,3681],{},[597,3678,913],{},[601,3680,916],{},[605,3682,607],{},[594,3684,3685,3687,3689,3691,3693,3695],{},[597,3686,913],{},[601,3688,3128],{"stretchy":2536},[3656,3690,3658],{},[597,3692,2549],{"mathvariant":733},[3656,3694,3658],{},[2307,3696,3697,3699],{},[597,3698,913],{},[597,3700,913],{},[601,3702,730],{},[2307,3704,3705,3723],{},[594,3706,3707,3709,3721],{},[601,3708,2537],{"fence":617},[901,3710,3711,3713],{},[597,3712,913],{},[594,3714,3715,3717,3719],{},[597,3716,913],{},[601,3718,916],{},[605,3720,607],{},[601,3722,2546],{"fence":617},[597,3724,913],{},[601,3726,2594],{},[901,3728,3729,3731],{},[605,3730,607],{},[597,3732,3408],{},[601,3734,603],{},[605,3736,607],{},[609,3738,3739],{"encoding":611},"\\frac{(n + 1)! \\, \u002F \\, (n + 1)^{n+1}}{n! \\, \u002F \\, n^n} = \\left( \\frac{n}{n + 1} \\right)^n \\to \\frac{1}{e} \u003C 1",[578,3741,3743,3945,4082,4159],{"className":3742,"ariaHidden":617},[616],[578,3744,3746,3749,3936,3939,3942],{"className":3745},[621],[578,3747],{"className":3748,"style":2617},[625],[578,3750,3752,3755,3933],{"className":3751},[630],[578,3753],{"className":3754},[952,1014],[578,3756,3758],{"className":3757},[901],[578,3759,3761,3925],{"className":3760},[961,962],[578,3762,3764,3922],{"className":3763},[966],[578,3765,3767,3819,3827],{"className":3766,"style":2636},[970],[578,3768,3769,3772],{"style":2639},[578,3770],{"className":3771,"style":1034},[978],[578,3773,3775,3778,3781,3784,3787,3790],{"className":3774},[630],[578,3776,913],{"className":3777},[630,631],[578,3779,3128],{"className":3780},[1182],[578,3782],{"className":3783,"style":2036},[635],[578,3785,2549],{"className":3786},[630],[578,3788],{"className":3789,"style":2036},[635],[578,3791,3793,3796],{"className":3792},[630],[578,3794,913],{"className":3795},[630,631],[578,3797,3799],{"className":3798},[1054],[578,3800,3802],{"className":3801},[961],[578,3803,3805],{"className":3804},[966],[578,3806,3808],{"className":3807,"style":2670},[970],[578,3809,3810,3813],{"style":2673},[578,3811],{"className":3812,"style":2351},[978],[578,3814,3816],{"className":3815},[1038,1039,1040,1041],[578,3817,913],{"className":3818},[630,631,1041],[578,3820,3821,3824],{"style":1094},[578,3822],{"className":3823,"style":1034},[978],[578,3825],{"className":3826,"style":1102},[1101],[578,3828,3829,3832],{"style":2693},[578,3830],{"className":3831,"style":1034},[978],[578,3833,3835,3838,3841,3844,3847,3850,3853,3857,3860,3863,3866,3869,3872,3875,3878,3881,3884],{"className":3834},[630],[578,3836,2537],{"className":3837},[952],[578,3839,913],{"className":3840},[630,631],[578,3842],{"className":3843,"style":2709},[635],[578,3845,916],{"className":3846},[1151],[578,3848],{"className":3849,"style":2709},[635],[578,3851,607],{"className":3852},[630],[578,3854,3856],{"className":3855},[1182],")!",[578,3858],{"className":3859,"style":2036},[635],[578,3861,2549],{"className":3862},[630],[578,3864],{"className":3865,"style":2036},[635],[578,3867,2537],{"className":3868},[952],[578,3870,913],{"className":3871},[630,631],[578,3873],{"className":3874,"style":2709},[635],[578,3876,916],{"className":3877},[1151],[578,3879],{"className":3880,"style":2709},[635],[578,3882,607],{"className":3883},[630],[578,3885,3887,3890],{"className":3886},[1182],[578,3888,2546],{"className":3889},[1182],[578,3891,3893],{"className":3892},[1054],[578,3894,3896],{"className":3895},[961],[578,3897,3899],{"className":3898},[966],[578,3900,3902],{"className":3901,"style":2743},[970],[578,3903,3904,3907],{"style":2347},[578,3905],{"className":3906,"style":2351},[978],[578,3908,3910],{"className":3909},[1038,1039,1040,1041],[578,3911,3913,3916,3919],{"className":3912},[630,1041],[578,3914,913],{"className":3915},[630,631,1041],[578,3917,916],{"className":3918},[1151,1041],[578,3920,607],{"className":3921},[630,1041],[578,3923,998],{"className":3924},[997],[578,3926,3928],{"className":3927},[966],[578,3929,3931],{"className":3930,"style":2773},[970],[578,3932],{},[578,3934],{"className":3935},[1182,1014],[578,3937],{"className":3938,"style":636},[635],[578,3940,730],{"className":3941},[640],[578,3943],{"className":3944,"style":636},[635],[578,3946,3948,3952,4073,4076,4079],{"className":3947},[621],[578,3949],{"className":3950,"style":3951},[625],"height:2.4543em;vertical-align:-0.95em;",[578,3953,3955,4048],{"className":3954},[948],[578,3956,3958,3966,4042],{"className":3957},[948],[578,3959,3963],{"className":3960,"style":3962},[952,3961],"delimcenter","top:0em;",[578,3964,2537],{"className":3965},[956,1040],[578,3967,3969,3972,4039],{"className":3968},[630],[578,3970],{"className":3971},[952,1014],[578,3973,3975],{"className":3974},[901],[578,3976,3978,4030],{"className":3977},[961,962],[578,3979,3981,4027],{"className":3980},[966],[578,3982,3985,4008,4016],{"className":3983,"style":3984},[970],"height:1.1076em;",[578,3986,3987,3990],{"style":2639},[578,3988],{"className":3989,"style":1034},[978],[578,3991,3993,3996,3999,4002,4005],{"className":3992},[630],[578,3994,913],{"className":3995},[630,631],[578,3997],{"className":3998,"style":2709},[635],[578,4000,916],{"className":4001},[1151],[578,4003],{"className":4004,"style":2709},[635],[578,4006,607],{"className":4007},[630],[578,4009,4010,4013],{"style":1094},[578,4011],{"className":4012,"style":1034},[978],[578,4014],{"className":4015,"style":1102},[1101],[578,4017,4018,4021],{"style":2693},[578,4019],{"className":4020,"style":1034},[978],[578,4022,4024],{"className":4023},[630],[578,4025,913],{"className":4026},[630,631],[578,4028,998],{"className":4029},[997],[578,4031,4033],{"className":4032},[966],[578,4034,4037],{"className":4035,"style":4036},[970],"height:0.7693em;",[578,4038],{},[578,4040],{"className":4041},[1182,1014],[578,4043,4045],{"className":4044,"style":3962},[1182,3961],[578,4046,2546],{"className":4047},[956,1040],[578,4049,4051],{"className":4050},[1054],[578,4052,4054],{"className":4053},[961],[578,4055,4057],{"className":4056},[966],[578,4058,4061],{"className":4059,"style":4060},[970],"height:1.5043em;",[578,4062,4064,4067],{"style":4063},"top:-3.9029em;margin-right:0.05em;",[578,4065],{"className":4066,"style":2351},[978],[578,4068,4070],{"className":4069},[1038,1039,1040,1041],[578,4071,913],{"className":4072},[630,631,1041],[578,4074],{"className":4075,"style":636},[635],[578,4077,2594],{"className":4078},[640],[578,4080],{"className":4081,"style":636},[635],[578,4083,4085,4088,4150,4153,4156],{"className":4084},[621],[578,4086],{"className":4087,"style":2794},[625],[578,4089,4091,4094,4147],{"className":4090},[630],[578,4092],{"className":4093},[952,1014],[578,4095,4097],{"className":4096},[901],[578,4098,4100,4139],{"className":4099},[961,962],[578,4101,4103,4136],{"className":4102},[966],[578,4104,4106,4117,4125],{"className":4105,"style":2813},[970],[578,4107,4108,4111],{"style":2639},[578,4109],{"className":4110,"style":1034},[978],[578,4112,4114],{"className":4113},[630],[578,4115,3408],{"className":4116},[630,631],[578,4118,4119,4122],{"style":1094},[578,4120],{"className":4121,"style":1034},[978],[578,4123],{"className":4124,"style":1102},[1101],[578,4126,4127,4130],{"style":2693},[578,4128],{"className":4129,"style":1034},[978],[578,4131,4133],{"className":4132},[630],[578,4134,607],{"className":4135},[630],[578,4137,998],{"className":4138},[997],[578,4140,4142],{"className":4141},[966],[578,4143,4145],{"className":4144,"style":2868},[970],[578,4146],{},[578,4148],{"className":4149},[1182,1014],[578,4151],{"className":4152,"style":636},[635],[578,4154,603],{"className":4155},[640],[578,4157],{"className":4158,"style":636},[635],[578,4160,4162,4165],{"className":4161},[621],[578,4163],{"className":4164,"style":650},[625],[578,4166,607],{"className":4167},[630],[564,4169,4170],{},"Die Reihe konvergiert.",[564,4172,4173,4174,4281,4282,4393,4394,4531,4532,4696,4697,4725],{},"Grenzfall: Für ",[578,4175,4177,4197],{"className":4176},[581],[578,4178,4180],{"className":4179},[585],[587,4181,4182],{"xmlns":589},[591,4183,4184,4194],{},[594,4185,4186,4188],{},[601,4187,2379],{},[901,4189,4190,4192],{},[605,4191,607],{},[597,4193,913],{},[609,4195,4196],{"encoding":611},"\\sum \\frac{1}{n}",[578,4198,4200],{"className":4199,"ariaHidden":617},[616],[578,4201,4203,4207,4210,4213],{"className":4202},[621],[578,4204],{"className":4205,"style":4206},[625],"height:1.1901em;vertical-align:-0.345em;",[578,4208,2379],{"className":4209,"style":2409},[2027,2407,2408],[578,4211],{"className":4212,"style":2036},[635],[578,4214,4216,4219,4278],{"className":4215},[630],[578,4217],{"className":4218},[952,1014],[578,4220,4222],{"className":4221},[901],[578,4223,4225,4270],{"className":4224},[961,962],[578,4226,4228,4267],{"className":4227},[966],[578,4229,4231,4245,4253],{"className":4230,"style":3304},[970],[578,4232,4233,4236],{"style":1030},[578,4234],{"className":4235,"style":1034},[978],[578,4237,4239],{"className":4238},[1038,1039,1040,1041],[578,4240,4242],{"className":4241},[630,1041],[578,4243,913],{"className":4244},[630,631,1041],[578,4246,4247,4250],{"style":1094},[578,4248],{"className":4249,"style":1034},[978],[578,4251],{"className":4252,"style":1102},[1101],[578,4254,4255,4258],{"style":2484},[578,4256],{"className":4257,"style":1034},[978],[578,4259,4261],{"className":4260},[1038,1039,1040,1041],[578,4262,4264],{"className":4263},[630,1041],[578,4265,607],{"className":4266},[630,1041],[578,4268,998],{"className":4269},[997],[578,4271,4273],{"className":4272},[966],[578,4274,4276],{"className":4275,"style":2506},[970],[578,4277],{},[578,4279],{"className":4280},[1182,1014]," ist der Quotient ",[578,4283,4285,4309],{"className":4284},[581],[578,4286,4288],{"className":4287},[585],[587,4289,4290],{"xmlns":589},[591,4291,4292,4306],{},[594,4293,4294],{},[901,4295,4296,4298],{},[597,4297,913],{},[594,4299,4300,4302,4304],{},[597,4301,913],{},[601,4303,916],{},[605,4305,607],{},[609,4307,4308],{"encoding":611},"\\frac{n}{n + 1}",[578,4310,4312],{"className":4311,"ariaHidden":617},[616],[578,4313,4315,4319],{"className":4314},[621],[578,4316],{"className":4317,"style":4318},[625],"height:1.0987em;vertical-align:-0.4033em;",[578,4320,4322,4325,4390],{"className":4321},[630],[578,4323],{"className":4324},[952,1014],[578,4326,4328],{"className":4327},[901],[578,4329,4331,4382],{"className":4330},[961,962],[578,4332,4334,4379],{"className":4333},[966],[578,4335,4337,4357,4365],{"className":4336,"style":2431},[970],[578,4338,4339,4342],{"style":1030},[578,4340],{"className":4341,"style":1034},[978],[578,4343,4345],{"className":4344},[1038,1039,1040,1041],[578,4346,4348,4351,4354],{"className":4347},[630,1041],[578,4349,913],{"className":4350},[630,631,1041],[578,4352,916],{"className":4353},[1151,1041],[578,4355,607],{"className":4356},[630,1041],[578,4358,4359,4362],{"style":1094},[578,4360],{"className":4361,"style":1034},[978],[578,4363],{"className":4364,"style":1102},[1101],[578,4366,4367,4370],{"style":2484},[578,4368],{"className":4369,"style":1034},[978],[578,4371,4373],{"className":4372},[1038,1039,1040,1041],[578,4374,4376],{"className":4375},[630,1041],[578,4377,913],{"className":4378},[630,631,1041],[578,4380,998],{"className":4381},[997],[578,4383,4385],{"className":4384},[966],[578,4386,4388],{"className":4387,"style":3356},[970],[578,4389],{},[578,4391],{"className":4392},[1182,1014],", für ",[578,4395,4397,4421],{"className":4396},[581],[578,4398,4400],{"className":4399},[585],[587,4401,4402],{"xmlns":589},[591,4403,4404,4418],{},[594,4405,4406,4408],{},[601,4407,2379],{},[901,4409,4410,4412],{},[605,4411,607],{},[2307,4413,4414,4416],{},[597,4415,913],{},[605,4417,2388],{},[609,4419,4420],{"encoding":611},"\\sum \\frac{1}{n^2}",[578,4422,4424],{"className":4423,"ariaHidden":617},[616],[578,4425,4427,4430,4433,4436],{"className":4426},[621],[578,4428],{"className":4429,"style":4206},[625],[578,4431,2379],{"className":4432,"style":2409},[2027,2407,2408],[578,4434],{"className":4435,"style":2036},[635],[578,4437,4439,4442,4528],{"className":4438},[630],[578,4440],{"className":4441},[952,1014],[578,4443,4445],{"className":4444},[901],[578,4446,4448,4520],{"className":4447},[961,962],[578,4449,4451,4517],{"className":4450},[966],[578,4452,4454,4495,4503],{"className":4453,"style":3304},[970],[578,4455,4456,4459],{"style":1030},[578,4457],{"className":4458,"style":1034},[978],[578,4460,4462],{"className":4461},[1038,1039,1040,1041],[578,4463,4465],{"className":4464},[630,1041],[578,4466,4468,4471],{"className":4467},[630,1041],[578,4469,913],{"className":4470},[630,631,1041],[578,4472,4474],{"className":4473},[1054],[578,4475,4477],{"className":4476},[961],[578,4478,4480],{"className":4479},[966],[578,4481,4484],{"className":4482,"style":4483},[970],"height:0.7463em;",[578,4485,4486,4489],{"style":2464},[578,4487],{"className":4488,"style":1071},[978],[578,4490,4492],{"className":4491},[1038,1075,1076,1041],[578,4493,2388],{"className":4494},[630,1041],[578,4496,4497,4500],{"style":1094},[578,4498],{"className":4499,"style":1034},[978],[578,4501],{"className":4502,"style":1102},[1101],[578,4504,4505,4508],{"style":2484},[578,4506],{"className":4507,"style":1034},[978],[578,4509,4511],{"className":4510},[1038,1039,1040,1041],[578,4512,4514],{"className":4513},[630,1041],[578,4515,607],{"className":4516},[630,1041],[578,4518,998],{"className":4519},[997],[578,4521,4523],{"className":4522},[966],[578,4524,4526],{"className":4525,"style":2506},[970],[578,4527],{},[578,4529],{"className":4530},[1182,1014]," ist er ",[578,4533,4535,4569],{"className":4534},[581],[578,4536,4538],{"className":4537},[585],[587,4539,4540],{"xmlns":589},[591,4541,4542,4566],{},[594,4543,4544],{},[2307,4545,4546,4564],{},[594,4547,4548,4550,4562],{},[601,4549,2537],{"fence":617},[901,4551,4552,4554],{},[597,4553,913],{},[594,4555,4556,4558,4560],{},[597,4557,913],{},[601,4559,916],{},[605,4561,607],{},[601,4563,2546],{"fence":617},[605,4565,2388],{},[609,4567,4568],{"encoding":611},"\\left(\\frac{n}{n + 1}\\right)^2",[578,4570,4572],{"className":4571,"ariaHidden":617},[616],[578,4573,4575,4579],{"className":4574},[621],[578,4576],{"className":4577,"style":4578},[625],"height:1.4573em;vertical-align:-0.4033em;",[578,4580,4582,4671],{"className":4581},[948],[578,4583,4585,4591,4665],{"className":4584},[948],[578,4586,4588],{"className":4587,"style":3962},[952,3961],[578,4589,2537],{"className":4590},[956,1076],[578,4592,4594,4597,4662],{"className":4593},[630],[578,4595],{"className":4596},[952,1014],[578,4598,4600],{"className":4599},[901],[578,4601,4603,4654],{"className":4602},[961,962],[578,4604,4606,4651],{"className":4605},[966],[578,4607,4609,4629,4637],{"className":4608,"style":2431},[970],[578,4610,4611,4614],{"style":1030},[578,4612],{"className":4613,"style":1034},[978],[578,4615,4617],{"className":4616},[1038,1039,1040,1041],[578,4618,4620,4623,4626],{"className":4619},[630,1041],[578,4621,913],{"className":4622},[630,631,1041],[578,4624,916],{"className":4625},[1151,1041],[578,4627,607],{"className":4628},[630,1041],[578,4630,4631,4634],{"style":1094},[578,4632],{"className":4633,"style":1034},[978],[578,4635],{"className":4636,"style":1102},[1101],[578,4638,4639,4642],{"style":2484},[578,4640],{"className":4641,"style":1034},[978],[578,4643,4645],{"className":4644},[1038,1039,1040,1041],[578,4646,4648],{"className":4647},[630,1041],[578,4649,913],{"className":4650},[630,631,1041],[578,4652,998],{"className":4653},[997],[578,4655,4657],{"className":4656},[966],[578,4658,4660],{"className":4659,"style":3356},[970],[578,4661],{},[578,4663],{"className":4664},[1182,1014],[578,4666,4668],{"className":4667,"style":3962},[1182,3961],[578,4669,2546],{"className":4670},[956,1076],[578,4672,4674],{"className":4673},[1054],[578,4675,4677],{"className":4676},[961],[578,4678,4680],{"className":4679},[966],[578,4681,4684],{"className":4682,"style":4683},[970],"height:1.054em;",[578,4685,4687,4690],{"style":4686},"top:-3.3029em;margin-right:0.05em;",[578,4688],{"className":4689,"style":2351},[978],[578,4691,4693],{"className":4692},[1038,1039,1040,1041],[578,4694,2388],{"className":4695},[630,1041],". Beide gehen gegen ",[578,4698,4700,4713],{"className":4699},[581],[578,4701,4703],{"className":4702},[585],[587,4704,4705],{"xmlns":589},[591,4706,4707,4711],{},[594,4708,4709],{},[605,4710,607],{},[609,4712,607],{"encoding":611},[578,4714,4716],{"className":4715,"ariaHidden":617},[616],[578,4717,4719,4722],{"className":4718},[621],[578,4720],{"className":4721,"style":650},[625],[578,4723,607],{"className":4724},[630],", aber die erste Reihe divergiert und die zweite konvergiert.",[559,4727,4729],{"id":4728},"typische-fehler","Typische Fehler",[572,4731,4732,4786,5117,5517],{},[575,4733,4734,4735,4785],{},"Aus ",[578,4736,4738,4755],{"className":4737},[581],[578,4739,4741],{"className":4740},[585],[587,4742,4743],{"xmlns":589},[591,4744,4745,4753],{},[594,4746,4747,4749,4751],{},[597,4748,599],{},[601,4750,730],{},[605,4752,607],{},[609,4754,793],{"encoding":611},[578,4756,4758,4776],{"className":4757,"ariaHidden":617},[616],[578,4759,4761,4764,4767,4770,4773],{"className":4760},[621],[578,4762],{"className":4763,"style":747},[625],[578,4765,599],{"className":4766},[630,631],[578,4768],{"className":4769,"style":636},[635],[578,4771,730],{"className":4772},[640],[578,4774],{"className":4775,"style":636},[635],[578,4777,4779,4782],{"className":4778},[621],[578,4780],{"className":4781,"style":650},[625],[578,4783,607],{"className":4784},[630]," auf Divergenz oder Konvergenz schließen. Das Kriterium ist dann unentschieden.",[575,4787,4788,4789,1239,5088,5116],{},"Nur ",[578,4790,4792,4833],{"className":4791},[581],[578,4793,4795],{"className":4794},[585],[587,4796,4797],{"xmlns":589},[591,4798,4799,4831],{},[594,4800,4801,4827,4829],{},[594,4802,4803,4805,4825],{},[601,4804,899],{"fence":617},[901,4806,4807,4819],{},[904,4808,4809,4811],{},[597,4810,908],{},[594,4812,4813,4815,4817],{},[597,4814,913],{},[601,4816,916],{},[605,4818,607],{},[904,4820,4821,4823],{},[597,4822,908],{},[597,4824,913],{},[601,4826,899],{"fence":617},[601,4828,603],{},[605,4830,607],{},[609,4832,1674],{"encoding":611},[578,4834,4836,5079],{"className":4835,"ariaHidden":617},[616],[578,4837,4839,4842,5070,5073,5076],{"className":4838},[621],[578,4840],{"className":4841,"style":944},[625],[578,4843,4845,4882,5033],{"className":4844},[948],[578,4846,4848],{"className":4847},[952],[578,4849,4851],{"className":4850},[956,957],[578,4852,4854,4874],{"className":4853},[961,962],[578,4855,4857,4871],{"className":4856},[966],[578,4858,4860],{"className":4859,"style":971},[970],[578,4861,4862,4865],{"style":974},[578,4863],{"className":4864,"style":979},[978],[578,4866,4867],{"style":982},[984,4868,4869],{"xmlns":986,"width":987,"height":988,"viewBox":989},[991,4870],{"d":993},[578,4872,998],{"className":4873},[997],[578,4875,4877],{"className":4876},[966],[578,4878,4880],{"className":4879,"style":1005},[970],[578,4881],{},[578,4883,4885,4888,5030],{"className":4884},[630],[578,4886],{"className":4887},[952,1014],[578,4889,4891],{"className":4890},[901],[578,4892,4894,5022],{"className":4893},[961,962],[578,4895,4897,5019],{"className":4896},[966],[578,4898,4900,4951,4959],{"className":4899,"style":1027},[970],[578,4901,4902,4905],{"style":1030},[578,4903],{"className":4904,"style":1034},[978],[578,4906,4908],{"className":4907},[1038,1039,1040,1041],[578,4909,4911],{"className":4910},[630,1041],[578,4912,4914,4917],{"className":4913},[630,1041],[578,4915,908],{"className":4916},[630,631,1041],[578,4918,4920],{"className":4919},[1054],[578,4921,4923,4943],{"className":4922},[961,962],[578,4924,4926,4940],{"className":4925},[966],[578,4927,4929],{"className":4928,"style":1064},[970],[578,4930,4931,4934],{"style":1067},[578,4932],{"className":4933,"style":1071},[978],[578,4935,4937],{"className":4936},[1038,1075,1076,1041],[578,4938,913],{"className":4939},[630,631,1041],[578,4941,998],{"className":4942},[997],[578,4944,4946],{"className":4945},[966],[578,4947,4949],{"className":4948,"style":1089},[970],[578,4950],{},[578,4952,4953,4956],{"style":1094},[578,4954],{"className":4955,"style":1034},[978],[578,4957],{"className":4958,"style":1102},[1101],[578,4960,4961,4964],{"style":1105},[578,4962],{"className":4963,"style":1034},[978],[578,4965,4967],{"className":4966},[1038,1039,1040,1041],[578,4968,4970],{"className":4969},[630,1041],[578,4971,4973,4976],{"className":4972},[630,1041],[578,4974,908],{"className":4975},[630,631,1041],[578,4977,4979],{"className":4978},[1054],[578,4980,4982,5011],{"className":4981},[961,962],[578,4983,4985,5008],{"className":4984},[966],[578,4986,4988],{"className":4987,"style":1133},[970],[578,4989,4990,4993],{"style":1067},[578,4991],{"className":4992,"style":1071},[978],[578,4994,4996],{"className":4995},[1038,1075,1076,1041],[578,4997,4999,5002,5005],{"className":4998},[630,1041],[578,5000,913],{"className":5001},[630,631,1041],[578,5003,916],{"className":5004},[1151,1041],[578,5006,607],{"className":5007},[630,1041],[578,5009,998],{"className":5010},[997],[578,5012,5014],{"className":5013},[966],[578,5015,5017],{"className":5016,"style":1164},[970],[578,5018],{},[578,5020,998],{"className":5021},[997],[578,5023,5025],{"className":5024},[966],[578,5026,5028],{"className":5027,"style":1176},[970],[578,5029],{},[578,5031],{"className":5032},[1182,1014],[578,5034,5036],{"className":5035},[1182],[578,5037,5039],{"className":5038},[956,957],[578,5040,5042,5062],{"className":5041},[961,962],[578,5043,5045,5059],{"className":5044},[966],[578,5046,5048],{"className":5047,"style":971},[970],[578,5049,5050,5053],{"style":974},[578,5051],{"className":5052,"style":979},[978],[578,5054,5055],{"style":982},[984,5056,5057],{"xmlns":986,"width":987,"height":988,"viewBox":989},[991,5058],{"d":993},[578,5060,998],{"className":5061},[997],[578,5063,5065],{"className":5064},[966],[578,5066,5068],{"className":5067,"style":1005},[970],[578,5069],{},[578,5071],{"className":5072,"style":636},[635],[578,5074,603],{"className":5075},[640],[578,5077],{"className":5078,"style":636},[635],[578,5080,5082,5085],{"className":5081},[621],[578,5083],{"className":5084,"style":650},[625],[578,5086,607],{"className":5087},[630],[578,5089,5091,5104],{"className":5090},[581],[578,5092,5094],{"className":5093},[585],[587,5095,5096],{"xmlns":589},[591,5097,5098,5102],{},[594,5099,5100],{},[597,5101,913],{},[609,5103,913],{"encoding":611},[578,5105,5107],{"className":5106,"ariaHidden":617},[616],[578,5108,5110,5113],{"className":5109},[621],[578,5111],{"className":5112,"style":766},[625],[578,5114,913],{"className":5115},[630,631]," prüfen. Bei der harmonischen Reihe gilt das auch, sie divergiert trotzdem.",[575,5118,5119,5120,5319,5320,5516],{},"Den Quotienten falsch herum bilden: ",[578,5121,5123,5155],{"className":5122},[581],[578,5124,5126],{"className":5125},[585],[587,5127,5128],{"xmlns":589},[591,5129,5130,5152],{},[594,5131,5132],{},[901,5133,5134,5140],{},[904,5135,5136,5138],{},[597,5137,908],{},[597,5139,913],{},[904,5141,5142,5144],{},[597,5143,908],{},[594,5145,5146,5148,5150],{},[597,5147,913],{},[601,5149,916],{},[605,5151,607],{},[609,5153,5154],{"encoding":611},"\\frac{a_n}{a_{n+1}}",[578,5156,5158],{"className":5157,"ariaHidden":617},[616],[578,5159,5161,5165],{"className":5160},[621],[578,5162],{"className":5163,"style":5164},[625],"height:1.1983em;vertical-align:-0.4868em;",[578,5166,5168,5171,5316],{"className":5167},[630],[578,5169],{"className":5170},[952,1014],[578,5172,5174],{"className":5173},[901],[578,5175,5177,5307],{"className":5176},[961,962],[578,5178,5180,5304],{"className":5179},[966],[578,5181,5184,5244,5252],{"className":5182,"style":5183},[970],"height:0.7115em;",[578,5185,5186,5189],{"style":1030},[578,5187],{"className":5188,"style":1034},[978],[578,5190,5192],{"className":5191},[1038,1039,1040,1041],[578,5193,5195],{"className":5194},[630,1041],[578,5196,5198,5201],{"className":5197},[630,1041],[578,5199,908],{"className":5200},[630,631,1041],[578,5202,5204],{"className":5203},[1054],[578,5205,5207,5236],{"className":5206},[961,962],[578,5208,5210,5233],{"className":5209},[966],[578,5211,5213],{"className":5212,"style":1133},[970],[578,5214,5215,5218],{"style":1067},[578,5216],{"className":5217,"style":1071},[978],[578,5219,5221],{"className":5220},[1038,1075,1076,1041],[578,5222,5224,5227,5230],{"className":5223},[630,1041],[578,5225,913],{"className":5226},[630,631,1041],[578,5228,916],{"className":5229},[1151,1041],[578,5231,607],{"className":5232},[630,1041],[578,5234,998],{"className":5235},[997],[578,5237,5239],{"className":5238},[966],[578,5240,5242],{"className":5241,"style":1164},[970],[578,5243],{},[578,5245,5246,5249],{"style":1094},[578,5247],{"className":5248,"style":1034},[978],[578,5250],{"className":5251,"style":1102},[1101],[578,5253,5255,5258],{"style":5254},"top:-3.4101em;",[578,5256],{"className":5257,"style":1034},[978],[578,5259,5261],{"className":5260},[1038,1039,1040,1041],[578,5262,5264],{"className":5263},[630,1041],[578,5265,5267,5270],{"className":5266},[630,1041],[578,5268,908],{"className":5269},[630,631,1041],[578,5271,5273],{"className":5272},[1054],[578,5274,5276,5296],{"className":5275},[961,962],[578,5277,5279,5293],{"className":5278},[966],[578,5280,5282],{"className":5281,"style":1064},[970],[578,5283,5284,5287],{"style":1067},[578,5285],{"className":5286,"style":1071},[978],[578,5288,5290],{"className":5289},[1038,1075,1076,1041],[578,5291,913],{"className":5292},[630,631,1041],[578,5294,998],{"className":5295},[997],[578,5297,5299],{"className":5298},[966],[578,5300,5302],{"className":5301,"style":1089},[970],[578,5303],{},[578,5305,998],{"className":5306},[997],[578,5308,5310],{"className":5309},[966],[578,5311,5314],{"className":5312,"style":5313},[970],"height:0.4868em;",[578,5315],{},[578,5317],{"className":5318},[1182,1014]," statt ",[578,5321,5323,5355],{"className":5322},[581],[578,5324,5326],{"className":5325},[585],[587,5327,5328],{"xmlns":589},[591,5329,5330,5352],{},[594,5331,5332],{},[901,5333,5334,5346],{},[904,5335,5336,5338],{},[597,5337,908],{},[594,5339,5340,5342,5344],{},[597,5341,913],{},[601,5343,916],{},[605,5345,607],{},[904,5347,5348,5350],{},[597,5349,908],{},[597,5351,913],{},[609,5353,5354],{"encoding":611},"\\frac{a_{n+1}}{a_n}",[578,5356,5358],{"className":5357,"ariaHidden":617},[616],[578,5359,5361,5365],{"className":5360},[621],[578,5362],{"className":5363,"style":5364},[625],"height:1.1983em;vertical-align:-0.4451em;",[578,5366,5368,5371,5513],{"className":5367},[630],[578,5369],{"className":5370},[952,1014],[578,5372,5374],{"className":5373},[901],[578,5375,5377,5505],{"className":5376},[961,962],[578,5378,5380,5502],{"className":5379},[966],[578,5381,5383,5434,5442],{"className":5382,"style":1027},[970],[578,5384,5385,5388],{"style":1030},[578,5386],{"className":5387,"style":1034},[978],[578,5389,5391],{"className":5390},[1038,1039,1040,1041],[578,5392,5394],{"className":5393},[630,1041],[578,5395,5397,5400],{"className":5396},[630,1041],[578,5398,908],{"className":5399},[630,631,1041],[578,5401,5403],{"className":5402},[1054],[578,5404,5406,5426],{"className":5405},[961,962],[578,5407,5409,5423],{"className":5408},[966],[578,5410,5412],{"className":5411,"style":1064},[970],[578,5413,5414,5417],{"style":1067},[578,5415],{"className":5416,"style":1071},[978],[578,5418,5420],{"className":5419},[1038,1075,1076,1041],[578,5421,913],{"className":5422},[630,631,1041],[578,5424,998],{"className":5425},[997],[578,5427,5429],{"className":5428},[966],[578,5430,5432],{"className":5431,"style":1089},[970],[578,5433],{},[578,5435,5436,5439],{"style":1094},[578,5437],{"className":5438,"style":1034},[978],[578,5440],{"className":5441,"style":1102},[1101],[578,5443,5444,5447],{"style":1105},[578,5445],{"className":5446,"style":1034},[978],[578,5448,5450],{"className":5449},[1038,1039,1040,1041],[578,5451,5453],{"className":5452},[630,1041],[578,5454,5456,5459],{"className":5455},[630,1041],[578,5457,908],{"className":5458},[630,631,1041],[578,5460,5462],{"className":5461},[1054],[578,5463,5465,5494],{"className":5464},[961,962],[578,5466,5468,5491],{"className":5467},[966],[578,5469,5471],{"className":5470,"style":1133},[970],[578,5472,5473,5476],{"style":1067},[578,5474],{"className":5475,"style":1071},[978],[578,5477,5479],{"className":5478},[1038,1075,1076,1041],[578,5480,5482,5485,5488],{"className":5481},[630,1041],[578,5483,913],{"className":5484},[630,631,1041],[578,5486,916],{"className":5487},[1151,1041],[578,5489,607],{"className":5490},[630,1041],[578,5492,998],{"className":5493},[997],[578,5495,5497],{"className":5496},[966],[578,5498,5500],{"className":5499,"style":1164},[970],[578,5501],{},[578,5503,998],{"className":5504},[997],[578,5506,5508],{"className":5507},[966],[578,5509,5511],{"className":5510,"style":1176},[970],[578,5512],{},[578,5514],{"className":5515},[1182,1014],". Dann kehren sich die Aussagen um.",[575,5518,5519,5520,5697,5698,2290],{},"Bei Fakultäten falsch kürzen: ",[578,5521,5523,5565],{"className":5522},[581],[578,5524,5526],{"className":5525},[585],[587,5527,5528],{"xmlns":589},[591,5529,5530,5562],{},[594,5531,5532,5554,5556,5558,5560],{},[901,5533,5534,5548],{},[594,5535,5536,5538,5540,5542,5544,5546],{},[601,5537,2537],{"stretchy":2536},[597,5539,913],{},[601,5541,916],{},[605,5543,607],{},[601,5545,2546],{"stretchy":2536},[601,5547,3128],{"stretchy":2536},[594,5549,5550,5552],{},[597,5551,913],{},[601,5553,3128],{"stretchy":2536},[601,5555,730],{},[597,5557,913],{},[601,5559,916],{},[605,5561,607],{},[609,5563,5564],{"encoding":611},"\\frac{(n + 1)!}{n!} = n + 1",[578,5566,5568,5669,5688],{"className":5567,"ariaHidden":617},[616],[578,5569,5571,5575,5660,5663,5666],{"className":5570},[621],[578,5572],{"className":5573,"style":5574},[625],"height:1.355em;vertical-align:-0.345em;",[578,5576,5578,5581,5657],{"className":5577},[630],[578,5579],{"className":5580},[952,1014],[578,5582,5584],{"className":5583},[901],[578,5585,5587,5649],{"className":5586},[961,962],[578,5588,5590,5646],{"className":5589},[966],[578,5591,5594,5611,5619],{"className":5592,"style":5593},[970],"height:1.01em;",[578,5595,5596,5599],{"style":1030},[578,5597],{"className":5598,"style":1034},[978],[578,5600,5602],{"className":5601},[1038,1039,1040,1041],[578,5603,5605,5608],{"className":5604},[630,1041],[578,5606,913],{"className":5607},[630,631,1041],[578,5609,3128],{"className":5610},[1182,1041],[578,5612,5613,5616],{"style":1094},[578,5614],{"className":5615,"style":1034},[978],[578,5617],{"className":5618,"style":1102},[1101],[578,5620,5622,5625],{"style":5621},"top:-3.485em;",[578,5623],{"className":5624,"style":1034},[978],[578,5626,5628],{"className":5627},[1038,1039,1040,1041],[578,5629,5631,5634,5637,5640,5643],{"className":5630},[630,1041],[578,5632,2537],{"className":5633},[952,1041],[578,5635,913],{"className":5636},[630,631,1041],[578,5638,916],{"className":5639},[1151,1041],[578,5641,607],{"className":5642},[630,1041],[578,5644,3856],{"className":5645},[1182,1041],[578,5647,998],{"className":5648},[997],[578,5650,5652],{"className":5651},[966],[578,5653,5655],{"className":5654,"style":2506},[970],[578,5656],{},[578,5658],{"className":5659},[1182,1014],[578,5661],{"className":5662,"style":636},[635],[578,5664,730],{"className":5665},[640],[578,5667],{"className":5668,"style":636},[635],[578,5670,5672,5676,5679,5682,5685],{"className":5671},[621],[578,5673],{"className":5674,"style":5675},[625],"height:0.6667em;vertical-align:-0.0833em;",[578,5677,913],{"className":5678},[630,631],[578,5680],{"className":5681,"style":2709},[635],[578,5683,916],{"className":5684},[1151],[578,5686],{"className":5687,"style":2709},[635],[578,5689,5691,5694],{"className":5690},[621],[578,5692],{"className":5693,"style":650},[625],[578,5695,607],{"className":5696},[630],", nicht ",[578,5699,5701,5714],{"className":5700},[581],[578,5702,5704],{"className":5703},[585],[587,5705,5706],{"xmlns":589},[591,5707,5708,5712],{},[594,5709,5710],{},[597,5711,913],{},[609,5713,913],{"encoding":611},[578,5715,5717],{"className":5716,"ariaHidden":617},[616],[578,5718,5720,5723],{"className":5719},[621],[578,5721],{"className":5722,"style":766},[625],[578,5724,913],{"className":5725},[630,631],{"title":5727,"searchDepth":5728,"depth":5728,"links":5729},"",2,[5730,5731,5732],{"id":561,"depth":5728,"text":562},{"id":2361,"depth":5728,"text":2362},{"id":4728,"depth":5728,"text":4729},[5734,5737,5741,5743,5748,5751,5756,5759,5762],{"lhs":5735,"rhs":5736},"((n + 1)\u002F2^(n + 1)) \u002F (n\u002F2^n)","(n + 1)\u002F(2*n)",{"lhs":5736,"rhs":5738,"where":5739},"0.5005",{"n":5740},1000,{"lhs":5742,"rhs":2388},"round(sum((1:60) .\u002F 2.^(1:60)), 9)",{"lhs":5744,"rhs":5745,"where":5746},"(2^(n + 1)\u002F(n + 1)!) \u002F (2^n\u002Fn!)","2\u002F(n + 1)",{"n":5747},7,{"lhs":5749,"rhs":5750},"round(sum(2.^(1:40) .\u002F (1:40)!), 9)","round(exp(2) - 1, 9)",{"lhs":5752,"rhs":5753,"where":5754},"((n + 1)!\u002F(n + 1)^(n + 1)) \u002F (n!\u002Fn^n)","(n\u002F(n + 1))^n",{"n":5755},6,{"lhs":5757,"rhs":5758},"round((1000\u002F1001)^1000, 3)","round(exp(-1), 3)",{"lhs":5760,"rhs":5761},"(1\u002F(n + 1)) \u002F (1\u002Fn)","n\u002F(n + 1)",{"lhs":5763,"rhs":5764},"(1\u002F(n + 1)^2) \u002F (1\u002Fn^2)","(n\u002F(n + 1))^2","a_n \\neq 0 \\text{ für alle hinreichend großen } n,\\ \\text{der Grenzwert } L \\text{ existiert}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a_n \\neq 0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">für alle hinreichend großen\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">der Grenzwert\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>L\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">L\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">L\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">existiert\u003C\u002Fspan>",null,"md","ratio-test","L = \\lim_{n \\to \\infty} \\left| \\frac{a_{n+1}}{a_n} \\right| \u003C 1 \\;\\Rightarrow\\; \\sum_{n=1}^{\\infty} a_n \\text{ konvergiert absolut}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>L\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmunder>\u003Cmrow>\u003Cmi>lim\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>→\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">∞\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmunder>\u003Cmrow>\u003Cmo fence=\"true\">∣\u003C\u002Fmo>\u003Cmfrac>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmfrac>\u003Cmo fence=\"true\">∣\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmo><\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmo>⇒\u003C\u002Fmo>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmunderover>\u003Cmo>∑\u003C\u002Fmo>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cmi mathvariant=\"normal\">∞\u003C\u002Fmi>\u003C\u002Fmunderover>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmtext> konvergiert absolut\u003C\u002Fmtext>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">L = \\lim_{n \\to \\infty} \\left| \\frac{a_{n+1}}{a_n} \\right| < 1 \\;\\Rightarrow\\; \\sum_{n=1}^{\\infty} a_n \\text{ konvergiert absolut}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">L\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.4em;vertical-align:-0.95em;\">\u003C\u002Fspan>\u003Cspan class=\"mop op-limits\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6944em;\">\u003Cspan style=\"top:-2.4em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003Cspan class=\"mrel mtight\">→\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">∞\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan>\u003Cspan class=\"mop\">lim\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen\">\u003Cspan class=\"delimsizing mult\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.45em;\">\u003Cspan class=\"pstrut\" style=\"height:4.4em;\">\u003C\u002Fspan>\u003Cspan style=\"width:0.333em;height:2.4em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.333em\" height=\"2.4em\" viewBox=\"0 0 333 2400\">\u003Cpath d=\"M145 15 v585 v1200 v585 c2.667,10,9.667,15,21,15\nc10,0,16.667,-5,20,-15 v-585 v-1200 v-585 c-2.667,-10,-9.667,-15,-21,-15\nc-10,0,-16.667,5,-20,15z M188 15 H145 v585 v1200 v585 h43z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.1076em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003Cspan class=\"mbin mtight\">+\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2083em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.836em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">\u003Cspan class=\"delimsizing mult\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.45em;\">\u003Cspan class=\"pstrut\" style=\"height:4.4em;\">\u003C\u002Fspan>\u003Cspan style=\"width:0.333em;height:2.4em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.333em\" height=\"2.4em\" viewBox=\"0 0 333 2400\">\u003Cpath d=\"M145 15 v585 v1200 v585 c2.667,10,9.667,15,21,15\nc10,0,16.667,-5,20,-15 v-585 v-1200 v-585 c-2.667,-10,-9.667,-15,-21,-15\nc-10,0,-16.667,5,-20,15z M188 15 H145 v585 v1200 v585 h43z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\"><\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">⇒\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.9185em;vertical-align:-1.2671em;\">\u003C\u002Fspan>\u003Cspan class=\"mop op-limits\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.6514em;\">\u003Cspan style=\"top:-1.8829em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003Cspan class=\"mrel mtight\">=\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.05em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan>\u003Cspan class=\"mop op-symbol large-op\">∑\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-4.3em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">∞\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.2671em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t 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