The simplest value of 1/(1 × 2)+1/(2 × 3)+1/(3 × 4)+…. +1/(9 × 10) is · ABC26GN1081
Subject: General Aptitude · Chapter: Simplification · Exam: P.C.S. 2008
The simplest value of $\frac{1}{1 \times 2}+\frac{1}{2 \times 3}+\frac{1}{3 \times 4}+\ldots$. $+\frac{1}{9 \times 10}$ is
(a)$\frac{1}{10}$
(b)$\frac{9}{10}$
(c)1
(d)10
Answer
Explanation
Given exp. $=\left(1-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+\ldots .+\left(\frac{1}{9}-\frac{1}{10}\right)$ $$=\left(1-\frac{1}{10}\right)=\frac{9}{10} .$$
Explanation as extracted from the printed page; notation may be imperfect.
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