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  • 一类积分

    (1)

    [sum_{k=1}^n frac{(-1)^k}{k}inom{n}{k} =sum_{k=1}^n(-1)^kinom{n}{k}int_0^1 x^{k-1} ext{d}x =-int_0^1sum_{k=1}^n inom{n}{k}(-x)^{k-1} ext{d}x =int_0^1frac{1-(1-x)^n}{-x} ext{d}x=-int_0^1frac{1-x^n}{1-x} =-int_0^1sum_{k=1}^n x^{k-1} ext{d}x=-sum_{k=1}^n frac{1}{k}]

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  • 原文地址:https://www.cnblogs.com/Math-Nav/p/13450209.html
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