Question

determine whether the series converges or diverges. Find the sum of the convergent series, if possible. e^(n+1)n^2/(n!), from 1 to infinity. SO far I have...

Answer 1

Yes, im stuck on : lim |e*n^2+2n+1 divided by n^3+n^2|

I think its 0, b/c the num< den.

Answer 2

\[\lim_{n \rightarrow \infty} \frac{e^{n+2}(n+1)^2}{(n+1)!}*\frac{n!}{e^{n+1}n^2}\]
\[=\lim_{n \rightarrow \infty} \frac{e}{n+1} \times \frac{(n+1)^2}{n^2}\] =0. Thus, the series is convergent. :D