Question

Dose the infinite geometric series diverge or converge? explain 3+9+27+81

Answer 1

The terms will be 3, 9, 27, 81 and so on.

notice, to get the next term, we simply multiply the current one by 3, namely the "common ratio" r = 3.

to make it plain and short, if 0 < | r | < 1, then the series sum will diverge, namely is approaching an explicit value, instead of just going on and on to infinity.

0 < | r | < 1, namely, if the common ratio is between 0 and 1, well a fraction, either negative or positive, only then the serie sum will diverge.  In this case is 3 and 3 is definitely not a fraction in that range.

Answer 2

Answer: The series diverges, and it does not have a sum.