Question
Does the infinite geometric series diverge or converge? Explain.
2 + 6 + 18 + 54 + ...
(1 point)
It diverges; it does not have a sum.
It converges; it does not have a sum.
It diverges; it has a sum.
It converges; it has a sum.
2 + 6 + 18 + 54 + ...
(1 point)
It diverges; it does not have a sum.
It converges; it does not have a sum.
It diverges; it has a sum.
It converges; it has a sum.
Answers
GPT 3.5
It diverges; it does not have a sum. The common ratio in this series is 3 (each term is multiplied by 3 to get the next term). Since the common ratio is greater than 1, the series will continue to increase without bound and therefore does not have a finite sum.