Question

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Answer 1

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.