# Precalculus : Sums of Infinite Series

## Example Questions

### Example Question #1 : Sums Of Infinite Series

Find the value for

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:

The series does not converge.

Explanation:

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

### Example Question #1 : Sums Of Infinite Series

Evaluate:

The series does not converge.

Explanation:

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

### Example Question #1 : Sums Of Infinite Series

What is the sum of the following infinite series?

diverges

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 #33 : Sequences And Series

What is the sum of the alternating series below?

Explanation:

The alternating series follows a geometric pattern.

We can evaluate the geometric series from the formula.

### Example Question #2 : Sums Of Infinite Series

Find the sum of the following infinite series: