Question

Does the infinite geometric series diverge or converge? Explain.

4+12+36+108+ ...

A. It converges; it does not have a sum

B. It diverges; it has a sum

C. It converges; it has a sum

D. It diverges; if does not have a sum

Answer 1

It diverges; it does not have a sum

Answer 2

Option D. is the correct option.

Explanation:

The given geometric series is 4+12+36+108.......infinite terms

Since any geometric series which is infinite in terms always diverges until unless it is in the form of fraction.

So we can not sum the terms of this series because the size of each term will increase with the number of terms.

Option D is the correct option.