n-1-e-n-n-n-n-

Question Number 104471 by Dwaipayan Shikari last updated on 21/Jul/20

\underset{n = 1}{\sum^{\infty}} \frac{e^{n} n!}{n^{n}}

Answered by MAB last updated on 21/Jul/20

l e t U_{n} = \frac{n!}{n^{n}} e^{n}

b y s t i r l i n g f o r m u l a : n! ∽ \sqrt{2 π n} {(\frac{n}{e})}^{n}

w e d e d u c e : U_{n} ∽ \sqrt{2 π n}

h e n c e \underset{n = 1}{\sum^{\infty}} \frac{e^{n} n!}{n^{n}} d i v e r g e s

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