If absx lt 1 ,then in the expansion of `(1+2x+3x^(2)+4x^(3)+...)^(1/2) ` ,the coefficient of `x^(n)` is

In the expansion of (1+x+x^(2)+x^(3)+x^(4))^(-2), coefficient of x^(10) is

In the expansion of (1+x+x^(2)+...oo)^(3) the coefficient of x^(n) is

Coefficient of x^(n) in the expansion of (1-2x+3x^(2)-4x^(3)+...oo)^(2) is

In the expansion of 2 log_(n) x- log_(n) (x+1) - log_(e)(x-1), the coefficient of x^(-4) is

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

What is the coefficient of x^(4) in the expansion of (1+2x+3x^(2)+4x^(3)+….)^(1//2) ?

If |x| lt 1 , then the coefficients of x^(n) in the expansion of (1 + x + x^(2) + x^(3) …)^(2) , is

The coefficient of x^(10) in the expansion of (1-2x+3x^(2)-4x^(3)+...oo)^(2) is

prove that the coefficient of x^(n) in the expansion of (1+x)^(2n) is twice the coefficient of x^(n) in the expansion of (1+x)^(2n-1)