In the expansion of `(x+a)^n`, the sums of the odd and the even terms are respectively P and Q, prove that `4PQ = (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 , 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 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 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 .

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

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