Answer
$1$
Work Step by Step
Here, we have: $ s_n=(1-\dfrac{1}{\sqrt 2})+(\dfrac{1}{\sqrt 2}-\dfrac{1}{\sqrt 3})+(\dfrac{1}{\sqrt k}-\dfrac{1}{\sqrt {k +1}})=1-\dfrac{1}{\sqrt {k+1}}$
Thus, we have the sum: $\lim\limits_{n \to \infty} s_n=\lim\limits_{n \to \infty} [1-\dfrac{1}{\sqrt {k+1}}]=\lim\limits_{n \to \infty}1- \lim\limits_{n \to \infty}\dfrac{1}{\sqrt {k+1}} =1$
