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.

Answer 1

[AI-generated answer — Bot 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.