Question

True or False
If the common ratio of a geometric series is less than one, then the sum of its terms has to be negative.

Answer 1

what do you think?

Answer 2

what if the common ratio is 1/2?

Answer 3

My notes say r ≠1 but I forgot what that meant

Answer 4

It's 2, right?

Answer 5

or is it 0.5

Answer 6

Example:

Geometric series with first term = 4; common ratio = 0.5
4 + 2 + 1 + 0.5 + 0.25 + ...
r is less than 1. Can this possibly add to a negative number?

Answer 7

@mathstudent55 The sum wont to a negative number. Does that mean that the only way that the sum will be negative if the common ratio itself is negative? Therefore, the statement is false?