Question

Does the following infinite geometric series diverge or converge? Explain.

Answer 1

Your answer is Diverge. To tell whether a series is divergent or convergent, you must look at the rate (the number it is being multiplied by) for the series.  If the rate is less than 1, then it would be convergent, meaning it does have a sum. If the rate is greater than 1, then that means it does not have a sum and never will. These series will diverge. Now your rate in this problem is 3 and 3 is greater than 1, so it diverges.