Arithmetic mean||G.P,Sum OF GP Series||Sum OF infinite series, Infinite series

Differentiation of infinite series

Basic OF Geometric Progression (GP)|| Sum OF n Terms || Sum OF Infinite Terms

The sum of an infinite geometric series is 2 and the sum of the geometric series made from the cubes of this infinite series is 24. Then the series is:

If |r|<1, then the sum of infinite terms of G.P is

The sum of first two terms of a G.P. is 5/3 and the sum to infinity of the series is 3. Find the first term :

If the sum of an infinite G.P is 32 and the some of its first two terms is 24, find the 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 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.