Geometric Series

The 1^(st) , 2^(nd) and 3^(rd) terms of an arithmetic series are a , b and a^(2) where 'a' is negative. The 1^(st) , 2^(nd) and 3^(rd) terms of a geometric series are a , a^(2) and b respectively. The sum of infinite geometric series is

The 1^st, 2^nd and 3^rd terms of an arithmetic series are a, b and a^2 where 'a' is negative. The 1^st, 2^nd and 3^rd terms of a geometric series are a, a^2 and b find the (a) value of a and b (b) sum of infinite geometric series if it exists. If no then find the sum to n terms of the G.P. (c) sum of the 40 term of the arithmetic series.

Let G Let G be the sum of infinite geometric series whose first term is sin theta and common ratio is cos theta, while G' be the sum of a different infinite geometric series whose first term cos theta and common ratio is sin theta. Find the number of solutions of the equation,G=G' in [0,2 pi] is

The 1^(st) , 2^(nd) and 3^(rd) terms of an arithmetic series are a , b and a^(2) where 'a' is negative. The 1^(st) , 2^(nd) and 3^(rd) terms of a geometric series are a , a^(2) and b respectively. The sum of the 40 terms of the arithmetic series is

Suppose x and y are real numbers such that -1 lt x lt y lt 1 Let G be the sum of the geometric series whose first term is x and whose common ratio is y, and let G' be the sum of the geomateric series whose first term is y and common ratio is x. If G = G' then the value of (x + y) is

Standard results|Some special series| Arithmetic geometric progression

If every term of a series in geometric progression is multiplied by a real number, then the resulting series also will be in geometric progression. [True/False]

The reciprocals of all the terms of a series in geometric progression form a ________ progression.

For a series in geometric progression, the first term is a and the second term is 3a. The common ratio of the series is _______.