Prove that the coefficient of `x^r` in the expansion of `(1-2x)^(-1/2)` is `(2r!)/[(2^r)(r!)^2]`

The coefficient of x^(r) in the expansion of (1-x)^(-2) is

the coefficient of x^(r) in the expansion of (1 - 4x )^(-1//2) , is

If |x|<(1)/(2), then the coefficient of x^(r) in the expansion of (1+2x)/((1-2x)^(2)) is

Let a_r denote the coefficient of y^(r-1) in the expansion of (1 + 2y)^(10) . If (a_(r+2))/(a_(r)) = 4 , then r is equal to

If n is an even natural number and coefficient of x^(r) in the expansion of ((1+x)^(n))/(1-x) is 2^(n) then (A) r>((n)/(2))(B)r>=((n-2)/(2))(C)r =n

Find the coefficient of x^(r) in the expansion of n of 1+(1+x)+(1+x)^(2)+......+(1+x)^(n)

If p_(r) is the coefficient of x^(r) in the expression of (1+x)^(2)(1+(x)/(2))^(2)...... then

If a_(r) is the coefficient of x^(r) in the expansion of (1+x+x^(2))^(n), then a_(1)-2a_(2)+3a_(3)....-2na_(2n)=

The coefficient of x^(r)[0<=r<=(n-1)] in lthe expansion of (x+3)^(n-1)+(x+3)^(n-2)(x+2)+(x+3)^(n-3)(x+2)^(2)+...+(x+2)^(n) is ^(n)C_(r)(3^(r)-2^(n)) b.^(n)C_(r)(3^(n-r)-2^(n-r)) c.^(n)C_(r)(3^(r)+2^(n-r)) d.none of these