Question

Does the infinite geometric series diverge or converge? Explain.

3 + 9 + 27 + 81 + ...

Answer 1

It diverges, as the terms get progressively larger for later terms in the sequence. A convergent series is one which approaches a minimum as the sequence progresses.

Answer 2

Ok how would we know if it has a sum or not?

Answer 3

For an infinite geometric series, if |r|>1 ,
then the sum diverges (means does not have sum or it means sum is infinite)

Answer 4

@WeNeedToTalk : @hartnn is correct. And that includes the case when r=1 as well - in which case S(inf)=inf(a), where a is the first term in the sequence.