Statement 1: The coefficient of `x^n` is `(1+x+(x^2)/(2!)+(x^3)/(3!)++(x^n)/(n !))^3` is `(3^n)/(n !)` Statement 2: The coefficient of `x^n ine^(3x)i s(3^n)/(n !)`

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

" The coefficient of "x^(n)" in "(1-x/(1!)+(x^2)/(2!)+..+((-1)^n(x^n))/(n !))^2

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

What is the coefficient of x^(n) in (x^(2) + 2x)^(n-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

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.

The coefficient of x^(n) in (1-(x)/(1!)+(x^(2))/(2!)-(x^(3))/(3!)+...+((-1)^(n)x^(n))/(n!))^(2) is equal to