Statement -1: The sum of the series
`(1)/(1!)+(2)/(2!)+(3)/(3!)+(4)/(4!)+..to infty` is e
Statement 2: The sum of the seies
`(1)/(1!)x+(2)/(2!)x^(2)+(3)/(3!)x^(3)+(4)/(4!)x^(4)..to infty is x e^(x)`

Options

A. 1
B. 2
C. 3
D. 4

Explanation

We have
`(1)/(1!)x+(2)/(2!)x^(2)+(3)/(3!)x^(3)+(1)/(4!)x^(4)+..to infty`
`=underset(n=1)overset(infty)Sigma (n)/(n!)x^(n)=x underset(n=1)overset(infty)Sigma(1)/(n-1)!x^(n-1)=xe^(x)`
So statement 2 is true
If we replace x by 1 in statement 2 then it reduces to statement 1 so statement 1 is also true and statement 2 is a correct explanation for statement -1