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

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 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 .

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.

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)

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) .

If the greatest term in the expansion of (1+x)^(2n) has the greatest coefficient if and only if xepsilon(10/11, 11/10) and the fourth term in the expansion of (kx+ 1/x)^m is n/4 then find the value of mk.

If x^p occurs in the expansion of (x^2+1/x)^(2n) , prove that its coefficient is : ((2n)!)/([1/3(4n-p)!][1/3(2n+p)!]) .

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

Show that , if the greatest term in the expansion of (1 + x)^(2n) has also the greatest coefficient then x lies between (n)/(n +1) " and" (n+1)/(n)

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