Determine whether the given series is convergent.
${\sum }_{n=1}^{\infty }\frac{1}{{}^{{}^5}\sqrt{n^3}}$

Explain why the integral test does not apply to the series.

${\sum }_{n=1}^{\infty }\frac{{(-1)}^n}{\ln n}$

Explain why the integral test does not apply to the series.

${\sum }_{n=4}^{\infty }\frac{1}{n+\sin n}$

Explain why the integral test does not apply to the series.

${\sum }_{n=0}^{\infty }\frac{n}{n^2-1}$

Confirm that the integral test applies and then use the integral test to determine convergence of the series.

(A) ${\sum }_{n=1}^{\infty }\frac{arc\tan n}{n^2+1}$ (B) ${\sum }_{n=1}^{\infty }\frac{1}{3n+2}$

Determine whether the given series is convergent.

${\sum }_{n=1}^{\infty }\frac{5}{3n-7}$

Determine whether the given series are convergent.

${\sum }_{n=1}^{\infty }\frac{n^e}{n^2}$

Determine whether the given series is convergent.

${\sum }_{n=1}^{\infty }{n}^{-1}+n^{-3}$

Use the Direct Comparison Test to determine whether the series converges.

${\sum }_{n=1}^{\infty }\frac{3}{\sqrt{n}-2}$