- #1

- 244

- 6

## Homework Statement

Determine the convergence or divergence of a

_{n}= n

^{p}/ e

^{n}

## The Attempt at a Solution

Using L'Hopitals Rule, I get (p(n

^{P-1}e

^{n}) - n

^{P}e

^{n}) / e

^{2n}which, if I take the limit as n [itex]\rightarrow[/itex][itex]\infty[/itex] I still get [itex]\infty/\infty[/itex] which doesn't help. I can see if a sequence converges to 0, i'm not sure how to show that it does, in general other than taking the limit or using L'Hopital.