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

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

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

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

If P_(r) is the coefficient of x^® in the expansion of (1 + x)^(2) (1 + (x)/(2))^(2) (1 + (x)/(2^(2)))^(2) (1 + (x)/(2^(3)))^(2)... prove that P_(r) = (2^(2))/((2^(r) -1))(P_(r-1) + P_(r-2) )and P_(4) = (1072)/(315) .

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

Find the coefficient of x^20 in the expression of (1+x^2)^40(x^2+2+1/x^2)^-5 .

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

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