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人気のある微分積分 >

sum from n=2 to infinity of 1/(n^2-1)

解

n = 2 \sum \infty \frac{1}{n ^{2} - 1}

解

\frac{3}{4}

+1

十進法表記

0.75

解答ステップ

n = 2 \sum \infty \frac{1}{n ^{2} - 1}

以下の部分分数を得る:

\frac{1}{n ^{2} - 1} : - \frac{1}{2 ( n + 1 )} + \frac{1}{2 ( n - 1 )}

= n = 2 \sum \infty - \frac{1}{2 ( n + 1 )} + \frac{1}{2 ( n - 1 )}

畳み込み級数を拡張する:

\frac{3}{4}

= \frac{3}{4}

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