Question
If \( S_{n}=\frac{1}{1+\sqrt{n}}+\frac{1}{2+\sqrt{2 n}}+\ldots+\frac{1}{n+\sqrt{n^{2}}}....
Question
\( \mathrm{P} \)
If \( S_{n}=\frac{1}{1+\sqrt{n}}+\frac{1}{2+\sqrt{2 n}}+\ldots+\frac{1}{n+\sqrt{n^{2}}} \) then \( \lim _{n \rightarrow \infty} S_{n} \) is equal to
\( 1 \quad \log _{e} 3 \)
\( 2 \quad 2+2 \log _{e} 2 \)
\( 3 \quad 2+\log _{e} 2 \)
\( 4 \quad 2 \log _{e} 2 \)
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