Question

Does the infinite geometric series diverge or converge? Explain.

2 + 6 + 18 + 54 + …
(1 point)
Responses

It diverges; it does not have a sum.
It diverges; it does not have a sum.

It converges; it does not have a sum.
It converges; it does not have a sum.

It diverges; it has 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. This is because the common ratio in this geometric series is 3 (each term is multiplied by 3 to get the next term), which is greater than 1. When the common ratio in a geometric series is greater than 1, the series diverges and does not have a finite sum.