Question

Determine whether the infinite geometric series converges or diverges.If it converges,find its sum.

Answer 1

Step 1:

Infinite geometric series :

The sum of the infinite geometric series is .

Where is first term,

           is the common ratio.

The infinite geometric series converges if .

Then its sum is .

Step 2:

The infinite geometric series is

The first term of the series is .

The second term of the series is .

The common ratio ,

.

Since , the series is converges.

The sum is  .

Substitute the values of and in above formula.

Sum

 

       

Solution:

The infinite geometric series is converges and its sum is .