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

解答

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

\frac{1}{2}

十进制

0.5

求解步骤

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

使用裂项级数审敛法:

\frac{1}{2}

= \frac{1}{2}

\int x^{\frac{- 2}{3}} x^{\frac{1}{3}} - 2 d x

\int \frac{d s}{s ^{2} ( s - 1 ) ^{2}} d x

\frac{d}{d x} (\frac{2}{x} - \frac{3 x}{3})

\frac{d}{d x} (\frac{x ^{3}}{4} + \frac{1}{3 x})

\int 2 d x