## divergent sum

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Math problems in Complex Analysis

### divergent sum

someone could to show how to demostrate the semiconvergent following sequences
$\sum _{m=1}^{\infty } (-e)^m=\frac{1-e}{2 (-2+\text{Sinh}[1])}$ and
$\sum _{m=1}^{\infty } (-1)^m \text{Log}\left[\frac{1}{2}+m\right]=\text{Log}\left[\frac{\sqrt{2} \text{Gamma}\left[\frac{5}{4}\right]}{\text{Gamma}\left[\frac{3}{4}\right]}\right]$
thanks
capea
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