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

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

Find the coefficient of x^n in the expansion of (1+ 2x + 3x^2 + 4x^3 + …..)^2

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.

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 |x|<1, then find the coefficient of x^n in the expansion of (1+x+x^2+x^3+....)^2dot

If, |x|<1,Find the coefficient of x^n in the expansion of (1+ 2x + 3x^2 + 4x^3 + …..)^(1/2)

If |x|<1, then find the coefficient of x^(n) in the expansion of (1+2x+3x^(2)+4x^(3)+...)^(1/2)

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

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

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