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 : 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 : 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

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.

If the fourth term in the expansion of (px+1/x)^n is 5/2 , then (n,p)=

If the sum of n terms of an A.P. is 3n^2 + 2n : Find the rth term.

If the 2nd, 3rd and 4th terms in the expansion of (x+a)^n are 240, 720 and 1080 respectively, find x ,\ a ,\ ndot

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