ABC26GN1083 · Simplification
Subject: General Aptitude · Chapter: Simplification · Exam: 2006 · Marks: · Difficulty:
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.
Open in whiteboard · Browse this chapter in the app