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.

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.

welshfella · Answer

what do you think?

welshfella · Answer

what if the common ratio is 1/2?

anonymous · Answer

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

anonymous · Answer

It's 2, right?

anonymous · Answer

or is it 0.5

mathstudent55 · Answer

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?

anonymous · Answer

@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?