Question

solve :-
$S_n=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}...+$ upto $99$ terms

Answer 1

$n^{th}$ term$=1/n(n+1)$

$=1/n-\left(\frac{1}{n+1}\right)$

$\Rightarrow S_n=\left[\right(1/1)-(1/2\left)\right]+\left[\right(1/2)-(1/3\left)\right]+\left[\right(1/3)-(1/4\left)\right]+\left[\right(1/4)-(1/5\left)\right]+.....$

$\Rightarrow S_n=1-1/(n-1)$

$\Rightarrow S_n=n/(n+1)$

Here $n=99$

$\Rightarrow S_n=99/99+1$

$\Rightarrow S_n=99/100$.