### All Precalculus Resources

## Example Questions

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

Find the value for

**Possible Answers:**

**Correct answer:**

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:**

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:

**Possible Answers:**

The series does not converge.

**Correct answer:**

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?

**Possible Answers:**

diverges

**Correct answer:**

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:**

The alternating series follows a geometric pattern.

We can evaluate the geometric series from the formula.

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

Find the sum of the following infinite series:

**Possible Answers:**

**Correct answer:**

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: