If S is the sum, P the product and R the sum of reciprocals of n terms of a G.P., then prove that `P^2 = (S/R)^n`.

If S_1 , S_2 and S_3 are respectively the sum of n, 2n and 3n terms of a G.P., then prove that S_1(S_3 - S_2) = (S_2 - S_1)^2 .

The sum of an infinite G.P is 5 and the sum of the squares of these terms is 15. Find the G.P.

The sum of an infinite G.P. is 5 and the sum of squares of these terms is 15, find the G.P.

Find the sum of the first n terms of an A.P. 1,4,7,10,…….. Also, find S_(40) .

If the sum of first p terms of an A.P is equal to the sum of the first q terms, then show that the sum of its first (p+q) terms is zero. (p ne q) .

If the sum of first p terms of an A.P is equal to the sum of first q terms, then show that the sum of its first (p+q) terms is zero . (p ne q) .

The sum of first n terms of a sequence is 5 (3^n -1) , show that it is a G,P.

If the first term of a G.P. is 2 and the sum of infinity is 6. Find the common ratio.

Find the sum of the first 5 terms of the G.P whose first term is 1 and common ration is 2/3.