Determine whether the series converges or diverges.

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Question

Determine whether the series converges or diverges.

(1) $\sum_{n=1}^{\infty} \frac{e^{1 / n}}{n^{2}}$

(2) $\sum_{n=1}^{\infty}\left(\frac{2}{\sqrt{n}}+\frac{(-1)^{n}}{3^{n+1}}\right)$

(3) $\sum_{n=1}^{\infty} \frac{5-2 \sin n}{n}$

(4) $\sum_{n=1}^{\infty} \frac{3+\cos n}{n^{3 / 2}}$

(5) $\sum_{n=0}^{\infty} \frac{\sqrt{n^{2}+2}}{n^{4}+n^{2}+5}$

(6) $\sum_{n=1}^{\infty=1}\left(1+\frac{1}{n}\right)^{n}$

(7) $\sum_{n=1}^{\infty} \frac{n+1}{n 2^{n}}$

(8) $\sum_{n=1}^{\infty} \frac{\arctan n}{n^{4}}$

(9) $\sum_{n=1}^{\infty} n \sin \frac{1}{n}$

math Advanced-Math

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Determine whether the series converges or diverges.

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