Originally Posted by

**anderson** hi everyone

need help with these questions.

Determine the series converges or diverges by using ratio test.

a) $\displaystyle \sum ^\infty _{n=1}$$\displaystyle \frac {(-10)^n}{n!}$

= $\displaystyle \frac {\frac {(-10)^{(n+1)}}{(n+1)!}}{\frac {(-10)^n}{n!}}$

=$\displaystyle \frac{-10}{n+1}$

the series converges.

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

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

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

i'm stuck on how to simplify,

really appreciate all your help & guidance.

thank you & regards.