The coefficient of `x^n` in the expansion of `(1-x)(1-x)^n` is `n-1` b. `(-1)^n(1-n)` c. `(-1)^(n-1)(n-1)^2` d. `(-1)^(n-1)n`

Coefficient of x^(n) in the expansion of ((1+x)^(n))/(1-x)

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

The coefficient of x^(n) y^(n) in the expansion of [(1 + x)(1+y) (x +y)]^(n) , is

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

The coefficients fo x^(n) in the expansion of (1+x)^(2n) and (1+x)^(2n-1) are in the ratio

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 (a). (n !)/((n-1)!(n+1)!) (b). ((2n)!)/((n-1)!(n+1)!) (c). ((2n)!)/((2n-1)!(2n+1)!) (d). none of these

The middle term in the expansion of (1 - (1)/(x))^(n) (1 - x)^(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.

If n is not a multiple of 3, then the coefficient of x^n in the expansion of log_e (1+x+x^2) is : (A) 1/n (B) 2/n (C) -1/n (D) -2/n