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

$$$$$$\text{You can't use 'macro parameter character \#' in math mode}$$$$\underset{n=0}{\sum ^{\mathrm{\infty }}}\frac{1}{n!+(n+1)!}=?$$$$$$

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

$$\underset{n=0}{\sum ^{\mathrm{\infty }}}\frac{1}{n!(n+2)}$$$$={\int }_0^1\underset{n=0}{\sum ^{\mathrm{\infty }}}\frac{x^{n+1}}{n!}dx={\int }_0^1{xe}^{x}dx={\left[(x-1)e^x\right]}_0^1=1$$

Commented by mnjuly1970 last updated on 04/Jul/21

$$\mathrm{thanks}\mathrm{alot}...$$

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