I am trying to check the convergence of the real infinite series $\sum \frac{n!e^{n}}{n^{n}}$. My problem is i tried for it ratio and root test both but both failed as in both case limit comes to $1$. Please give me a hint for its convergence.Thaks a lot.
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The series does not converge. – Cornman Oct 04 '17 at 16:06
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How please give some hint..... – neelkanth Oct 04 '17 at 16:07
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Use Stirling's formula: https://en.wikipedia.org/wiki/Stirling%27s_approximation – carmichael561 Oct 04 '17 at 16:08
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I want some simple solution ....... – neelkanth Oct 04 '17 at 16:09
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Yes it's really very nice thanks a lot..... – neelkanth Oct 04 '17 at 16:16