# Does the series sum_(n=1)^oo (n+5)/(nsqrt(n+3)) converges of diverges

Does the series $\sum _{n=1}^{\mathrm{\infty }}\frac{n+5}{n\sqrt{n+3}}$ converges of diverges
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unett
$\frac{n+5}{n\sqrt{n+3}}\ge \frac{n}{n\sqrt{n+3}}\ge \frac{1}{\sqrt{n+3}}$
$\sum _{n=1}^{\mathrm{\infty }}\frac{n+5}{n\sqrt{n+3}}\ge \sum _{n=1}^{\mathrm{\infty }}\frac{1}{\sqrt{n+3}}$
Since $\sum _{n=1}^{\mathrm{\infty }}\frac{1}{\sqrt{n+3}}$ is a divergent series, therefore $\sum _{n=1}^{\mathrm{\infty }}\frac{n+5}{n\sqrt{n+3}}$ is divergent.