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人気のある微分積分 >

sum from n=0 to infinity of 1/(n(n+2))

解

n = 0 \sum \infty \frac{1}{n ( n + 2 )}

解

\frac{3}{4}

+1

十進法表記

0.75

解答ステップ

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

以下の部分分数を得る:

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

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

畳み込み級数を拡張する:

\frac{3}{4}

= \frac{3}{4}

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