Use the divergence test to determine if the following series diverge or state that the test is inconclusive. 
${\sum }_{n=1}^{\infty }\sin \left(\frac{n\pi }{2}\right)$

Determine the convergence or divergence of the series. 

${\sum }_{k=1}^{\infty }\frac{{(-1)}^{k}4}{3k+2}$

Determine the convergence or divergence of the series. 

${\sum }_{n=1}^{\infty }\frac{5^{n-1}}{2^n}$

Determine the convergence or divergence of the series. 

${\sum }_{n=1}^{\infty }\frac{n\bullet 8^n}{(n+1)!}$

Determine the convergence or divergence of the series. 

${\sum }_{k=1}^{\infty }\frac{7k^2}{5k+3}$

Use the divergence test to determine if the following series diverge or state that the test is inconclusive. 

${\sum }_{n=1}^{\infty }\frac{{10}^n}{n!}$

Use the divergence test to determine if the following series diverge or state that the test is inconclusive. 

${\sum }_{n=1}^{\infty }\frac{n^2}{n(n^2-1000)}$

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.

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