Statement 1: The coefficient of `x^n` in `(1+x+(x^2)/(2!)+(x^3)/(3!)++(x^n)/(n !))^3` is `(3^n)/(n !)`. Statement 2: The coefficient of `x^n` in `e^(3x)` is `(3^n)/(n !)`

Options

A. `(3^(n))/(n!)`
B. `(3^(n-1))/(n!)`
C. `(3^(n))/((n-1)!)`
D. `(1)/(3^(n).n!)`

Answer

A

Explanation

Coefficient of `x^(n)` in `(1+x+(x^(2))/(2!)+(x^(3))/(3!) + "……" + (x^(n))/(n!))^(3)`
=Cofficient of `x^(n)` in `(1+x+(x^(2))/(2!) + "….." (x^(n))/(n!) + "…..")^(3)`
(as higher powers of x are not considered while calculating the coefficient of `x^(n)`)
`=` Coefficient of `x^(n)` in `e^(3x) = (3^(n))/(n!)`