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Question Number 161353 by HongKing last updated on 16/Dec/21

$$\mathrm{Prove}\mathrm{that}:$$$$\underset{\mathbf{n}=0}{\sum ^{\mathrm{\infty }}}\frac{{(-1)}^{\mathbf{n}}}{2\mathrm{n}+1}\underset{0}{\stackrel{1}{\int }}\underset{0}{\stackrel{1}{\int }}\frac{\mathrm{dxdy}}{{({\mathrm{x}}^2+{\mathrm{y}}^2)}^{\mathbf{n}}}=\frac{2}{3}$$

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