In the expansion of `(x +a)^n`, the sums of the odd and the even terms are O and E respectively, prove that : `O^2-E^2= (x^2-a^2)^n`.

In the expansion of (x +a)^n , the sums of the odd and the even terms are O and E respectively, prove that : 2(O^2+E^2)=(x+a)^(2n)+(x-a)^(2n) .

In the expansion of (x +a)^n , the sums of the odd and the even terms are O and E respectively, prove that : 4OE=(x+a)^(2n)-(x-a)^(2n) .

In the expansion of (x+a)^n if the sum of odd terms is P and the sum of even terms is Q , then a. P^2-Q^2=(x^2-a^2)^n b. 4P Q=(x+a)^(2n)-(x-a)^(2n) c. 2(P^2+Q^2)=(x+a)^(2n)+(x-a)^(2n) d. none of these

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

If the first and the nth term of a G.P. are a and b. respectively, and if P is the product of n terms, prove that P^2 = (ab)^n .

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

If the fourth term in the expansion of (a x+1/x)^n is 5/2 , then find the values of a and n.

Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that P^2R^n = S^n .

Find the sum to n terms of the series given below whose nth terms is given by n^2 + 2^n

Find the sum of n terms of the series whose nth term is given by n^2+2^n