Precalculus : Sums of Infinite Series

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #1 : Finding Sums Of Infinite Series

Find the value for 

Possible Answers:

Correct answer:

Explanation:

To best understand, let's write out the series. So

We can see this is an infinite geometric series with each successive term being multiplied by .

A definition you may wish to remember is

 where  stands for the common ratio between the numbers, which in this case is  or . So we get

 

Example Question #1 : Sums Of Infinite Series

Evaluate:

Possible Answers:

The series does not converge.

Correct answer:

Explanation:

This is a geometric series whose first term is   and whose common ratio is . The sum of this series is:

Example Question #25 : Sequences And Series

Evaluate:

Possible Answers:

The series does not converge.

Correct answer:

Explanation:

This is a geometric series whose first term is   and whose common ratio is . The sum of this series is:

Example Question #2 : Sums Of Infinite Series

What is the sum of the following infinite series?

Possible Answers:

diverges

Correct answer:

Explanation:

This series is not alternating - it is the mixture of two geometric series.

The first series has the positive terms.

The second series has the negative terms.

The sum of these values is 3.5.

Example Question #2 : Sums Of Infinite Series

What is the sum of the alternating series below?

Possible Answers:

Correct answer:

Explanation:

The alternating series follows a geometric pattern.

We can evaluate the geometric series from the formula.

Example Question #3 : Sums Of Infinite Series

Find the sum of the following infinite series:

 

Possible Answers:

Correct answer:

Explanation:

Notice that this is an infinite geometric series, with ratio of terms = 1/3. Hence it can be rewritten as:

Since the ratio, 1/3, has absolute value less than 1, we can find the sum using this formula:

Where  is the first term of the sequence. In this case , and thus:

 

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