Correct Answer:
Second Option
Solution:
A geometric series converges when the value of its common ratio is between -1 and 1. Else the series will diverge. So we find the common ratio for each of the given options, the series with common ratio between -1 and 1 will be converging series.
For first option, common ratio = 1/3 divided by 1/9 = 3
Common ratio is not between -1 and 1, so this series is diverging.
For second option, common ratio = 1/2 divided by 1 = 1/2
Since the common ratio is between -1 and 1, this series is converging.
For third option, common ratio = -4
This series is also diverging.
For Fourth option, common ratio = 2
This series is also diverging.