Thursday, 10 August 2017

sequences and series - How do I evaluate this sum :$ sum_{n=1}^{infty}frac{{(-1)}^{n-1}log n}{n^s}$?

How do I evaluate this sum :$$ \sum_{n=1}^{\infty}\frac{{(-1)}^{n-1}\log n}{n^s}$$




Note : In wolfram alpha it is convergent for $Re(s)>1$ .!!



Thank you for any help

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