Does the infinite geometric series diverge or converge? Explain.

Question

2 + 6 + 18 + 54 + …

Answer 1

The given infinite geometric series has a common ratio of 3 (each term is 3 times the previous term).

For a geometric series to converge, the absolute value of the common ratio should be less than 1. In this case, the common ratio is 3, which is greater than 1. Therefore, the infinite geometric series 2 + 6 + 18 + 54 + … diverges.