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

0 votes

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

asked Feb 16, 2015 in PRECALCULUS by anonymous
reshown Feb 16, 2015 by goushi

1 Answer

0 votes

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 .

answered Feb 23, 2015 by yamin_math Mentor

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