Precalculus : Sums of Infinite Series

Example Questions

Example Question #1 : Finding 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 #34 : Sequences And 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 #35 : 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 #1 : Sums Of Infinite Series

Find the sum of the following infinite series:       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: All Precalculus Resources 