Answer
$5$
Work Step by Step
Consider $a_n=\dfrac{5}{n(n+1)}$
or, $a_n=\dfrac{5}{n}-\dfrac{5}{n+1}$
Formula to calculate the Nth partial sum of a geometric series is
$s_n=\dfrac{a(1-r^n)}{1-r}$
Formula to calculate the Sum of a geometric series can be found as:
$S=\dfrac{a}{1-r}$
Now, we have, $s_n= (5-\dfrac{5}{2})-(\dfrac{5}{2}-\dfrac{5}{3})+....(\dfrac{5}{n}-\dfrac{5}{n+1})=[5-\dfrac{5}{n+1}]$
Also,$\lim\limits_{n \to \infty} s_n=5$
