5. Infinite GM and its sum

Infinite GM and its sum

The sum of an infinite Geometric Progression whose first term 'a' and common ratio 'r' (-1 < r < 1 i.e., |r| < 1) is

S = a/(1−r)

Proof:

A series of the form a + ar + ar22 + ...... + arnn + ............... ∞ is called an infinite geometric series.

Let us consider an infinite Geometric Progression with first term a and common ratio r, where -1 < r < 1 i.e., |r| < 1. Therefore, the sum of n terms of this Geometric Progression in given by

Example: Find the sum to infinity of the Geometric Progression

Example:. If the p^th and q^th terms of a G.P. are q and p respectively, show that its (p + q)^th term is 

Solution:

Hence the proof.