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`.

Find the coefficient of x^(8) in the expansion of (1-2x)^(- 1/2) .

The coefficient of x^(n) in expansion of (1 + x)(1 - x)^(n) is

Find the coefficient of x^5 in the expansion of (1+x^2)^5 (1+x)^4

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

The coefficient of x^(n) in the expansion of (1 - 9x + 20x^(2))^(-1) is

If the sum of the coefficients in the expansion of (1 -3x + 10x^2)^(n) is a and the sum of the coefficients in the expansion of (1 - x^(2))^(n) is b , then

if the sum of coefficients in the expansion of (x-2y+3z)^n is 128, then find the greatest coefficients in the expansion of (1+x)^ndot

If the sum of the coefficients in the expansion of (a + b)^(n) is 4096, then the greatest coefficient in the expansion is