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Question Number 6335 by FilupSmith last updated on 24/Jun/16
Can you show me why:  1−(1/2)+(1/3)−(1/4)+...=ln(2)  or  Σ_(n=1) ^∞ (((−1)^(n+1) )/n)=ln(2)
$$\mathrm{Can}\:\mathrm{you}\:\mathrm{show}\:\mathrm{me}\:\mathrm{why}: \\ $$$$\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{4}}+…=\mathrm{ln}\left(\mathrm{2}\right) \\ $$$$\mathrm{or} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} }{{n}}=\mathrm{ln}\left(\mathrm{2}\right) \\ $$

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