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 !)`

Find the coefficient of x^n in (1+x/(1!)+(x^2)/(2!)+........+(x^n)/(n !))^2 .

Coefficient of x^15 in (1+ x + x^3+ x^4)^n is

Statement-1: The middle term of (x+(1)/(x))^(2n) can exceed ((2n)^(n))/(n!) for some value of x. Statement-2: The coefficient of x^(n) in the expansion of (1-2x+3x^(2)-4x^(3)+ . . .)^(-n) is (1*3*5 . . .(2n-1))/(n!)*2^(n) . Statement-3: The coefficient of x^(5) in (1+2x+3x^(2)+ . . .)^(-3//2) is 2.1.

Let n be a natureal number and 0ltxlt1 Statement 1: The coefficient of x^(n) in log (1)/(1+x+x^(2)) is (1)/(n) when n is not a multiple of 3 Statement 2: The coefficient of x^(n) in log(1)/(1-x+x^(2)-x^(3)) is (1)/(n) when n is an odd natural number

Coefficient of x^n in (1+x)/(1!) +((1+x)^2)/(2!) + ((1+x)^3)/(3!) + .......=

The coefficient of x^(n) in the expansion of ((1+x)^(2))/((1 - x)^(3)) , is

The coefficient of x^(n) in the expansion of (1)/((1-x)(3 -x)) , is

The coefficient of x^(n-2) in the polynomial (x-1)(x-2)(x-3)...(x-n) is

If the coefficient of x^11 and x^12 in (2+ (8x)/(3))^n are equal find n

The sum of the coefficients in the expansion of (1 - x + x^(2) - x^(3))^(n) ,is