True or False:
In the expansion of `(1+x)^(2n), n in N`, the coefficient of `x^(n-1)` and `x^(n+1)` are equal.

In the expansion of (1+x)^n , the coefficient of x^(p-1) and of x^(q-1) are equal. Show that p+q=n+2, p ne q .

The middle term in the expansion of (1 + x)^(2n) is :

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

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

Show 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) .

In the expansion of (x^(2) + 1 + (1)/(x^(2)))^(n), n in N ,

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

Statement-I : In the expansion of (1+ x)^n ifcoefficient of 31^(st) and 32^(nd) terms are equal then n = 61 Statement -II : Middle term in the expansion of (1+x)^n has greatest coefficient.

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