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Question Number 206393 by MaruMaru last updated on 13/Apr/24

$$\mathrm{find}\mathrm{S}=1+\sum _{\ell }\frac{{(-)}^{\ell }}{\ell }(\frac{1}{\ell }-\frac{1}{\ell +1}),\ell \in [1,\mathrm{\infty })$$$$1+\sum _{\ell }\frac{{(-)}^{\ell }}{\ell }(\frac{1}{\ell }-\frac{1}{\ell +1})$$$$1-(1-\frac{1}{2})+\frac{1}{2}(\frac{1}{2}-\frac{1}{3})-\frac{1}{3}(\frac{1}{3}-\frac{1}{4})+\frac{1}{4}(\frac{1}{4}-\frac{1}{5})-......$$

Answered by MaruMaru last updated on 17/Apr/24

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