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k-2-1-k-lnk-k-ln2-1-2-ln-2-2-




Question Number 148020 by qaz last updated on 25/Jul/21
Σ_(k=2) ^∞ (−1)^k ∙((lnk)/k)=γln2−(1/2)ln^2 2
$$\underset{\mathrm{k}=\mathrm{2}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{\mathrm{k}} \centerdot\frac{\mathrm{lnk}}{\mathrm{k}}=\gamma\mathrm{ln2}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}^{\mathrm{2}} \mathrm{2} \\ $$

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