Question

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

Answer 1

It's false because you could have a series converge to a positive value. There is no set rule that it has to be negative

IF it said `If the common ratio of a geometric series is less than one, then the sum converges` then the statement would be true.

Answer 2

More specifically, the common ratio r has to make this inequality true

|r| < 1

for the infinite geometric series to converge

Answer 3

That's exactly what I was thinking but I just wanted to be 100% sure. Thank you!

Answer 4

you're welcome