Calculus-n-0-1-n-n-1-

Question Number 145319 by mnjuly1970 last updated on 04/Jul/21

You can't use 'macro parameter character #' in math mode

\underset{n = 0}{\sum^{\infty}} \frac{1}{n! + (n + 1)!} = ?

Answered by Dwaipayan Shikari last updated on 04/Jul/21

\underset{n = 0}{\sum^{\infty}} \frac{1}{n! (n + 2)}

= \int_{0}^{1} \underset{n = 0}{\sum^{\infty}} \frac{x^{n + 1}}{n!} d x = \int_{0}^{1} {x e}^{x} d x = {[(x - 1) e^{x}]}_{0}^{1} = 1

Commented by mnjuly1970 last updated on 04/Jul/21

thanks alot \dots