Answer
$S_n=\sqrt{1}-\sqrt{n+1}$
Work Step by Step
We know that
$a_n=\sqrt n-\sqrt{n+1}$
First term is given as $a_1=\sqrt{1}-\sqrt{2}$
Second term is given as $a_2=\sqrt{2}-\sqrt{3}$
Third term is given as $a_3=\sqrt{3}-\sqrt{4}$
Fourth term is given as $a_4=\sqrt{4}-\sqrt{5}$
Now $S_1=a_1=\sqrt{1}-\sqrt{2}$
$S_2=a_1+a_2=\sqrt{1}-\sqrt{3}$
$S_3=a_1+a_2+a_3=\sqrt{1}-\sqrt{4}$
$S_4=a_1+a_2+a_3+a_4=\sqrt{1}-\sqrt{5}$
Thus, $S_n=\sqrt{1}-\sqrt{n+1}$