Inverse factorial summation

Question

Find the sum $$\sum_{n=0}^\infty \dfrac1{n!}$$

Sorry, I couldn't find the symbol for Sigma.

Sigma(1/n!) I tried this but couldn't do it.

Any suggestions for the problem are welcome.

The sign you are searching is \sum. Is this sum finite, or infinite? — Cornman, Dec 19 '19 at 11:21
Not really sure about the range of the sum . Please check if the edit is correct — The Demonix _ Hermit, Dec 19 '19 at 11:22
By the way , $e = 1 + \frac1{2!} + \frac1{3!} + \frac1{4!} + \cdots$ — The Demonix _ Hermit, Dec 19 '19 at 11:24
This is a well-known number, usually designated by the letter $e.$ — Allawonder, Dec 19 '19 at 11:37
Your question is indeed ambiguous -- what do you mean by finding the sum. It's already there. The most important thing is to find out if it represents a definite number, or not. It does. Whatever is left to do is to find ways to approximate this number (which is irrational, by the way) by rationals. We know how to do all this. Check a book on calculus, or google $e.$ — Allawonder, Dec 19 '19 at 11:39

score 1 · Accepted Answer · answered Dec 19 '19 at 12:04

1

$$e^x=\sum_{n=0}^{+\infty}\dfrac{x^n}{n!}$$ So for $x=1$ you have: $$e=\sum_{n=0}^{+\infty}\dfrac{1}{n!}$$

answered Dec 19 '19 at 12:04

Riccardo.Alestra

score 0 · Answer 2 · edited Dec 19 '19 at 11:31

0

The answere is the number e. Just use the Taylor-Lagrange theorem on the exponential fonction.

edited Dec 19 '19 at 11:31

J. W. Tanner

answered Dec 19 '19 at 11:25

shocop

2 Answers2