Question

infinite summation :

1 + (1+2)/2! + (1+2+3)/3! ........

Answer 1

or in other words
1/2 * summation ( n(n+1)/n! ) from n=1 or 0 ,,to infinity..

Answer 2

Something * e

Answer 3

\[e^x=\sum_{n=0}^{\infty} \frac{x^n}{n!}\]take derivative\[e^x=\sum_{n=1}^{\infty} \frac{nx^{n-1}}{n!}\]multiply by x^2\[x^2e^x=\sum_{n=1}^{\infty} \frac{nx^{n+1}}{n!}\]and ...

Answer 4

another derivative and then put x=1 !!
thanks a lot!!