A weird limit involving e and 1/n

Hi, I'm working on a problem but stuck at a weird looking limit:

It is suppose to converge to but:

I wrote the limit as

and as

But neither are useful as I know the rule is and I can't seem to get them down to something like that.

Any hints? Thank you!

Re: A weird limit involving e and 1/n

Re: A weird limit involving e and 1/n

Hey tttcomrader.

Hint: e^(-a-log(n)) = e^(-a)/n. Check the limit of lim n-> infinity [1 + b/n]^n (should be e^b if memory serves me correctly).