Saturday, 22 April 2017

real analysis - The convergence of sumin=1nfty(1)nleft(fracneright)nfrac1n!

I'm trying to figure out if the n=1(1)n(ne)n1n! converges or not. I've tried the Leibnitz test for alternating series, but it leads to Stirling's formula and I was wondering if there's any other way so I could avoid using it. I'll be grateful for any idea.

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real analysis - How to find limhrightarrow0fracsin(ha)h

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