If n is a positive integer and r is a nonnegative integer, prove that the coefficients of `x^r` and `x^(n-r)` in the expansion of `(1+x)^(n)` are equal.

If n is an odd positive integer, prove that the coefficients of the middle terms in the expansion of (x+y)^n are equal.

If the coefficients of (r-5)^th and (2r - 1)^th terms in the expansion of (1 + x)^34 are equal, find r.

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

r and n are positive integers r gt 1 , n gt 2 and coefficient of (r + 2)^(th) term and 3r^(th) term in the expansion of (1 + x)^(2n) are equal, then n equals

Prove that the coefficient of x^n in the expansion of 1/((1-x)(1-2x)(1-3x))i s1/2(3^(n+2)-2^(n+3)+1)dot

In the expansion of (1+a)^m+n , prove that coefficients of a^m and a^n are equal.