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}$

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

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

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

=$\displaystyle e^{2n} +{e^2}$

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