Is (n!/n^n)*exp^n a Convergent or Divergent Summation?

[adiputra]

1)summation for n=0 to infinity for (n!/n^n)*exp^n. Can anyone help to prove whether this is convergent or divergent?

 

[mathman]

1)summation for n=0 to infinity for (n!/n^n)*exp^n. Can anyone help to prove whether this is convergent or divergent?

Can you refer to Stirling's formula? When you use it, the n term in the sequence is approximately (2(pi)n)^1/2. The series could never converge, with the individual terms getting larger.

 

[adiputra]

thank a lot