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Question Number 141581 by qaz last updated on 20/May/21

$$\underset{n=0}{\sum ^{\mathrm{\infty }}}{\int }_0^1\frac{x^n}{1+x}dx=?$$

Commented by Dwaipayan Shikari last updated on 20/May/21

$${\int }_0^1\frac{1}{1-x^2}dx\Rightarrow Diverges$$

Answered by mindispower last updated on 20/May/21

$$\widehat{⩾}\sum _{n⩾0}{\int }_0^1\frac{x^n}{2}dx=\sum _{n⩾0}\frac{1}{2(n+1)}\to \mathrm{\infty }$$

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