Question

Does the infinite geometric series diverge or converge?
2+6+18+54+...

Answer 1

The common ratio in this series is 3 (each term is 3 times the previous term).

To determine if the infinite geometric series converges, we need to test if the absolute value of the common ratio is less than 1.

|3| < 1

Since the absolute value of the common ratio is less than 1, the infinite geometric series converges.