Question

The sum of the series
`(1)/(1!)+(2)/(2!)+(3)/(3!)+(4)/(4!)`+…..to `infty` is
A. e
B. 2e
C. `(1)/(2)e`
D. none of these

Answer 1

Answer:
We have
`1+(1)/(1!)+(2)/(2!)+(3)/(3!)+…= underset(n=1)overset(infty)Sigma(nb)/(n!)=underset(n=1)overset(infty)Sigma(1)/(n-1)!=e`