prove-that-lim-n-1-n-1-p-2-n-1-p-pln-p-1-p-1-ln-pi-

Tinku Tara August 29, 2023 Coordinate Geometry 0 Comments

Question Number 196674 by Erico last updated on 29/Aug/23

prove that lim_(n→+∞) (−1)^(n−1) +Σ_(p=2) ^n (−1)^p pln(((p+1)/(p−1)))=ln(π)

$$\mathrm{prove}\:\mathrm{that}\: \\ $$$$\underset{\mathrm{n}\rightarrow+\infty} {\mathrm{lim}}\:\left(−\mathrm{1}\right)^{\mathrm{n}−\mathrm{1}} +\underset{\mathrm{p}=\mathrm{2}} {\overset{\mathrm{n}} {\sum}}\left(−\mathrm{1}\right)^{\mathrm{p}} \mathrm{pln}\left(\frac{\mathrm{p}+\mathrm{1}}{\mathrm{p}−\mathrm{1}}\right)=\mathrm{ln}\left(\pi\right) \\ $$

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prove-that-lim-n-1-n-1-p-2-n-1-p-pln-p-1-p-1-ln-pi-

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