
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.