Problems solving a limit: (1+1/n)^(n^2) * e^(-n) as n->infinite

[FraMar]

Hi,

I can't get this limit right (1+1/n)^(n^2) * e^(-n) as n->infinite

it should be e^(1/2), but when I try it the result is 1...what am I getting wrong?

(my last step is e^n * e^(-n)=1)

 

[stapel]

I can't get this limit right (1+1/n)^(n^2) * e^(-n) as n->infinite

I think the above means the following:

. . . . .\(\displaystyle \displaystyle \lim_{n \rightarrow \infty}\, \left[\left(1\, +\, \dfrac{1}{n}\right)^{n^2}\, \times\, e^{-n}\right]\)

Is this correct?

it should be e^(1/2)...

If my version of the limit (above) is correct, then Wolfram's Alpha engine disagrees with what the limit "should" be: here

...when I try it the result is 1...what am I getting wrong?

Unfortunately, it is not possible for us to troubleshoot work that we cannot see. Kindly please reply with a clear listing of your efforts, leading to the answer you got. Thank you!