Which geometric series converges? a. 1/2 + 1/4 + 1/8 + 1/16 + b. 1/2 + 1 + 2 + 4 + c. 1/2 + 3/2+ 9/2+ 27/2+ d. 1/2 + 3 + 18 + 108 +

Option: A is the correct answer.

          A)      

Step-by-step explanation:

We know that a geometric series of the type:

where

converges if r<1

Hence, we will check in each of the given options for which r<1

B)

From this series we observe that the common ratio i.e. r=2

Since,

and so on.

Hence, the series is not convergent.

Hence, option: B is incorrect.

C)

From this series we observe that the common ratio i.e. r=3>1

Hence, the series diverges.

Hence, option: C is false.

D)

In this geometric series trhe common ratio is: 6>1

Hence, the series does not converge.

Hence, option D is incorrect.

A)

Here we have:

         common ratio i.e. r=1/2<1

Hence, the geometric series converge and the sum is given by:

         Hence, option: A is correct.

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