Question

$\frac{1}{1.2}$ + $\frac{1}{2.3}$ + $\frac{1}{3.4}$ +.......+ ......... $\frac{1}{n.(n+1)}$ equals

• A. $\frac{1}{n(n+1)}$
• B. $\frac{n}{n+1}$
• C. $\frac{2n}{n+1}$
• D. $\frac{2}{n(n+1)}$

Answer 1

The correct option is B

$\frac{n}{n+1}$

( $\frac{1}{1}$ - $\frac{1}{2}$) + ( $\frac{1}{2}$ - $\frac{1}{3}$) + ( $\frac{1}{3}$ - $\frac{1}{4}$) + .........+ ( $\frac{1}{n}$ - $\frac{1}{n+1}$)

= 1 - $\frac{1}{n+1}$ = $\frac{n}{n+1}$