In the binomial expansion of `(1+a)^(m+n)` , prove that the coefficient of `a^m a n d\ a^n` are equal.

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

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

In the binomial expansion of (a+b)^n , coefficients of the fourth and thirteenth terms are equal to each other. Find n .

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

In the binomial expansion of (1+x)^n , coefficients of the fifth, sixth and seventh terms are in A.P. find all the values of n for which this can happen.

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)

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)

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)

If in the expansion of (1 + x)^n , the coefficients of pth and qth terms are equal, prove that p+q=n+ 2 , where p!=q .

Prove that the coefficient of the middle term in the expansion of (1+x)^(2n) is equal to the sum of the coefficients of middle terms in the expansion of (1+x)^(2n-1)