if the coefficients of `x,x^2 and x^3` in the binomial expansion `(1+x)^(2n)` are in arithmetic progression then prove that `2n^2-9n+7=0`

The coeffiicent of x^(n) in the binomial expansion of ( 1-x)^(-2) is

If the coefficients of a^(r-1),a^(r) and in the expansion of in the expansion of are in arithmetic progression,prove that n^(2)-n(4r+1)+4r^(2)-2=0

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

Find the sum of the coefficient of to middle terms in the binomial expansion of (1+x)^(2n-1)

The coefficient of x^(n) in the expansion of ((1+x)^(2))/((1 - x)^(3)) , is