Given the two series

$A=1+\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+\frac{1}{25}+$dots, and $,B={\displaystyle \underset{n=1}{\overset{}{}}}{n}^5{e}^{-n^6}.$

determine whether each series $is$ convergent $or$ divergent and choose the correct

statement.

Both series are convergent.

Series $Ais$ divergent, series $Bis$ convergent.

Series $Ais$ convergent, series $Bis$ divergent.

Both series are divergent.