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

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

The coefficient of x in the expansion of (1 + x)(1 + 2x)(1 + 3x) ... (1 + 100x) is

The coefficient of x^(4) in the expansion of (1 + x + x^(2) + x^3)^(11) is

Prove that the coefficient of x^n in the expansion of 1/((1-x)(1-2x)(1-3x))i s1/2(3^(n+2)-2^(n+3)+1)dot

The coefficient of 1//x in the expansion of (1+x)^n(1+1//x)^n is (n !)/((n-1)!(n+1)!) b. ((2n)!)/((n-1)!(n+1)!) c. ((2n)!)/((2n-1)!(2n+1)!) d. none of these

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

If |x| lt 1 , then the coefficient of x^(5) in the expansion of (1+ 2x + 3x^(2) + ..........)^((-3)/2) is