(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Does [tex]\sum _{ n=1 }^{ \infty }{ \frac { { \alpha }^{ n }{ n }! }{ { n }^{ n } } } [/tex] converge [tex]\forall |\alpha |<e[/tex]

and if so, how can I prove it?

2. Relevant equations

[tex]{ e }^{ x }=\sum _{ n=0 }^{ \infty }{ \frac { { x }^{ n } }{ n! } } [/tex]

3. The attempt at a solution

In the case of e I get the strange and probably wrong [tex]\sum _{ n=1 }^{ \infty }{ \frac { { (\sum _{ n=0 }^{ \infty }{ \frac { 1 }{ n! } } ) }^{ n }{ n }! }{ { n }^{ n } } } [/tex]

which seems to be the boundary between convergence and divergence for the series, but I have no idea how to actually make anything of this.

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# Homework Help: Infinite series convergence question:

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