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Question-163469




Question Number 163469 by Zaynal last updated on 07/Jan/22
Commented by smallEinstein last updated on 07/Jan/22
Answered by amin96 last updated on 07/Jan/22
Ω=−Σ_(n=1) ^∞ (1/n)∫_0 ^1 x^(n−1) dx=−Σ_(n=1) ^∞ (1/n^2 )=−ζ(2)
$$\Omega=−\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}}\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{{n}−\mathrm{1}} {dx}=−\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\mathrm{2}} }=−\zeta\left(\mathrm{2}\right) \\ $$

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