Chapter 12.2, Problem 4CFU

To determine

To give the counter example for the given statement.

Explanation of Solution

Given:

The statement is “The sum of geometric series cannot be less than its first term”.

Calculation:

The counter example for the above statement is as below

For any geometric sequence having first term negative and common ratio is positive integer, the sum of geometric sequence is less than its first term

Let us consider the sequence having first term $a=-2$ and common ratio $r=2$ with four terms

  $2,-4,8,-16$

The sum of the above geometric sequence is $-10$ , which is less than its first term $2$ .