Does the infinite geometric series diverge or converge? Explain

2+6+18+54+...

1 answer

The given series is 2+6+18+54+...

To determine if this series converges or diverges we can calculate the common ratio, r.

r = 6/2 = 3

Since the common ratio, r, is greater than 1, the series diverges. This can also be seen by observing that the terms of the series keep increasing with no bound.
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