If `pa n dq` are ositive, then prove that the coefficients of `x^pa n dx^q` in the expansion of `(1+x)^(p+q)` will be equal.

Statement-If a in N, then the cofficient of x^(3) and x^(a) in (1+3x+3x^(2)+x^(3))(1+x)^(a) are equal.Statement-II:If p and q be positive integers,then the coefficients of x^(p) and x^(q) in the expansion of (1+x)^(p+q) will be equal.

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

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

The coefficient of x^(n) in the expansion of log_(a)(1+x) is

Coefficient of x^(n) in the expansion of ((1+x)^(n))/(1-x)

Let a_(r) denote the coefficient of x^(r) in the expansion of ( 1 + x)^(P + q) , then

If m and n are positive integers, then prove that the coefficients of x^(m) " and " x^(n) are equal in the expansion of (1+x)^(m+n)