Answer
$S_{n}=1-\sqrt {\left( n+1\right) }$
$\Rightarrow S_{1}=1-\sqrt 2$
$\Rightarrow S_{2}=1-\sqrt 3$
$\Rightarrow S_{3}=-1$
$\Rightarrow S_{4}=1-\sqrt 5$
Work Step by Step
$S_{1}=a_1=\sqrt {1}-\sqrt {2}$
$S_{2}=a_{1}+a_{2}=\left( \sqrt {1}-\sqrt {2}\right) +\left( \sqrt {2}-\sqrt {3}\right) =\sqrt {1}-\sqrt {3}$
$S_{3}=a_{1}+a_{2}+a_{3}=\left( \sqrt {1}-\sqrt {2}\right) +\left( \sqrt {2}-\sqrt {3}\right) +\left( \sqrt {3}-\sqrt {4}\right) =\sqrt {1}-\sqrt {4}=-1$
$S_{4}=a_{1}+a_{2}+a_{3}+a_{4}=\left( \sqrt {1}-\sqrt {2}\right) +\left( \sqrt {2}-\sqrt {3}\right) +\left( \sqrt {3}-\sqrt {4}\right) +\left( \sqrt {4}-\sqrt {5}\right) =\sqrt {1}-\sqrt {5}$
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$S_{n}=1-\sqrt {\left( n+1\right) }$
