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Question Number 123650 by Dwaipayan Shikari last updated on 27/Nov/20

$$1-\frac{1}{4}+\frac{1}{8}-\frac{1}{10}+\frac{1}{14}-\frac{1}{16}+...$$

Commented by MJS_new last updated on 27/Nov/20

$$\mathrm{sorry}\mathrm{I}\mathrm{misread}\mathrm{it}...$$

Commented by Dwaipayan Shikari last updated on 27/Nov/20

$$Howdoyoufinditsir?$$

Commented by MJS_new last updated on 27/Nov/20

$$=1-\mathrm{\Sigma }\frac{1}{4+6n}+\mathrm{\Sigma }\frac{1}{8+6n}=$$$$=1-\frac{1}{9}\mathrm{\Sigma }\frac{1}{n^2+2n+8/9}=1-(\frac{1}{2}-\frac{\sqrt{3}}{18}\pi )=$$$$=\frac{\sqrt{3}}{18}\pi +\frac{1}{2}$$

Commented by Dwaipayan Shikari last updated on 27/Nov/20

$$Yessir!ihavealsofind\frac{1}{2}+\frac{\pi }{6\sqrt{3}}$$

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