In the expansion of `(1+x+x^2+...oo)^3` the coefficient of `x^n` is

In the expansion of (1+x+x^2+x^3+…..oo)^3, coefficient of x^3 is

In the expansion of (1+x+x^2+x^3+…..oo)^3, coefficient of x^3 is

Prove that in the expansion of (1+x)^(2n) , the coefficient of x^n is double the coefficient of x^n in the expansion of frac{(1+2x+x^2)^n}{1+x}

If in the expansion of (1+ x )^(m) (1-x) ^(n) the coefficient of x and x ^(2) are 3 and (-6) respectively, then the value of n is-

If n is a positive integer and the coefficient of x^10 in the expansion of (1 + x)^15 is equal to the coefficient of x^5 in the expansion of (1-x)^(-n) then n =

prove that the coefficient of x^n in the expansion of (1+x)^(2n) is twice the coefficient of x^n in the expansion of (1+x)^(2n-1)