Answer
$1$
Work Step by Step
The Nth partial sums are:$ s_n=(1-\dfrac{1}{\sqrt 2})+(\dfrac{1}{\sqrt 2}-\dfrac{1}{\sqrt 3})+(\dfrac{1}{\sqrt n}-\dfrac{1}{\sqrt {n +1}})=1-\dfrac{1}{\sqrt {n+1}}$
Now, $\lim\limits_{n \to \infty} s_n=\lim\limits_{n \to \infty} [1-\dfrac{1}{\sqrt {k+1}}]$
or, $=\lim\limits_{n \to \infty}1- \lim\limits_{n \to \infty}\dfrac{1}{\sqrt {k+1}} $
or, $=1$
