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Question Number 80814 by mathmax by abdo last updated on 06/Feb/20

$$findnatureoftheserie\sum _{n=1}^{\mathrm{\infty }}(1-cos\left(\frac{\pi }{n}\right))$$

Commented by mind is power last updated on 06/Feb/20

$$cos\left(\frac{\pi }{n}\right)=1-\frac{{\pi }^2}{2n^2}+o\left(\frac{1}{n^2}\right)$$$$\Rightarrow 1-cos\left(\frac{\pi }{n}\right)\sim \frac{{\pi }^2}{2n^2}cvRiemann$$

Commented by mathmax by abdo last updated on 06/Feb/20

$$thankssir.$$

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