1 / 12

# 9-2 Series - PowerPoint PPT Presentation

9-2 Series. AP Calculus Miss Battaglia. Summing Series. An infinite series (or just a series for short) is simply adding up the infinite number of terms of a sequence. Consider: The series associated with the sequence is:.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about '9-2 Series' - kirkan

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### 9-2 Series

AP Calculus

Miss Battaglia

• An infinite series (or just a series for short) is simply adding up the infinite number of terms of a sequence. Consider:

The series associated with the sequence is:

Partial Sums more compact form:

Continuing with the same series, look at how the sum grows by listing the “sum” of one term, two terms, three terms, etc.

The nth partial sum, Sn, of an infinite series is the sum of the first n terms of the series.

If you list the partial sums, you have a sequence of partial sums.

The Main Event: Convergence and Divergence of a Series more compact form:

If the sequence of partial sums converges, you say that the series converges; otherwise, the sequence of partial sums diverges and you say that the series diverges.

A no-brainer divergence test: more compact form: The nth term test

Geometric Series more compact form:

A geometric series is a series of the form:

The first term, a, is called the leading term. Each term after the first equals the preceding term multiplied by r, which is called the ratio.

Ex: a = 5 and r = 3

Geometric Series Rule more compact form:

If 0 < |r| < 1, the geometric series

converges to . If |r| > 1, the series

diverges.

Ex: a = 5 and r = 3

Telescoping Series more compact form:

To see that this is a telescoping series you have to use partial fractions.

A telescoping series will converge iffbn approaches a finite number as n∞. Moreover, if the series converges it sum is

Writing a Series in Telescoping Form more compact form:

Find the sum of the series

Homework more compact form:

• P. 614 #9, 12, 17, 18, 37, 39, 43, 45, 51, 59, 61, 68, 69, 70, 71, 72, 74