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人気のある微分積分 >

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

解

n = 0 \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}

人気の例

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

n = 1 \sum \infty \frac{n !}{n \cdot 2 ^{n}}

sum from n=1 to infinity of 1/(25n^2+5n-6)

n = 1 \sum \infty \frac{1}{25 n ^{2} + 5 n - 6}

sum from n=0 to infinity of (-1)^n 1/n

n = 0 \sum \infty (- 1)^{n} \frac{1}{n}

sum from n=2 to infinity of 3/(n(n+3))

n = 2 \sum \infty \frac{3}{n ( n + 3 )}

sum from n=1 to infinity of 1/(n^2+30)

n = 1 \sum \infty \frac{1}{n ^{2} + 30}