Determine the series is absolutely convergent or diverges by using ratio test.

b) $\displaystyle \sum ^\infty _{n=1}$$\displaystyle {(1+\frac{1}{n})}^{n^2}$

$\displaystyle \frac {{(1+\frac{1}{n+1})}^{(n+1)^2}}{{(1+\frac{1}{n})}^ {n^2}}$

=$\displaystyle \frac {{(1+\frac{1}{n+1})}^{n^2}+{(1+\frac{1}{n+1})}^{2n }+{(1+\frac{1}{n+1})}^{2}}{{(1+\frac{1}{n})}^{n^2} }$

=$\displaystyle \frac{e^2+e^ne^n+1}{e^2}$

is that the final answer? can it be simplified any further?

how do i simplifly this question,please help. really appreaciate all your help & support