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