When simplified, the sum 1/2+1/6+1/12+1/20+1/30+ ….+1/(n(n+1)) is equal to · ABC26GN1083
Subject: General Aptitude · Chapter: Simplification · Exam: S.S.C. 2006
When simplified, the sum $\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+$ $\ldots .+\frac{1}{n(n+1)}$ is equal to
(a)$\frac{1}{n}$
(b)$\frac{1}{n+1}$
(c)$\frac{n}{n+1}$
(d)$\frac{2(n-1)}{n}$
Answer
Explanation
Given exp. $=\left(1-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{5}\right)$ $$\begin{aligned} & +\ldots . .+\left(\frac{1}{n}-\frac{1}{n+1}\right) \\ = & \left(1-\frac{1}{n+1}\right)=\frac{n}{n+1} \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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