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n-0-0-1-x-n-1-x-dx-




Question Number 141581 by qaz last updated on 20/May/21
Σ_(n=0) ^∞ ∫_0 ^1 (x^n /(1+x))dx=?
$$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{{n}} }{\mathrm{1}+{x}}{dx}=? \\ $$
Commented by Dwaipayan Shikari last updated on 20/May/21
∫_0 ^1 (1/(1−x^2 ))dx ⇒Diverges
$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\mathrm{1}−{x}^{\mathrm{2}} }{dx}\:\Rightarrow{Diverges} \\ $$
Answered by mindispower last updated on 20/May/21
≥^� Σ_(n≥0) ∫_0 ^1 (x^n /2)dx=Σ_(n≥0) (1/(2(n+1)))→∞
$$\hat {\geqslant}\underset{{n}\geqslant\mathrm{0}} {\sum}\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{{n}} }{\mathrm{2}}{dx}=\underset{{n}\geqslant\mathrm{0}} {\sum}\frac{\mathrm{1}}{\mathrm{2}\left({n}+\mathrm{1}\right)}\rightarrow\infty \\ $$

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