Use the Integral Test to determine if the series shown below converges or diverges. Be sure to check that the conditions of the Integral Test are satisfied.

${\displaystyle \underset{n=1}{\overset{}{}}}\frac{4n^2}{e^{\frac{n}{2}}}$

Select the correct choice below and fill in the answer box to complete your choice.

A$.$ The series converges because ${\displaystyle \underset{4}{\overset{}{}}}\frac{4x^2}{e^{\frac{x}{2}}}dx=$

$($Type an exact answer.$)$

B$.$ The series diverges because ${\displaystyle \underset{4}{\overset{}{}}}\frac{4x^2}{e^{\frac{x}{2}}}dx=$

$($Type an exact answer.$)$

c$.$

The Integral Test cannot be used since one or more of the conditions for the Integral Test is not satisfied.