1 / 7

One important application of infinite sequences is in representing “infinite summations.”

Infinite Series. One important application of infinite sequences is in representing “infinite summations.” Informally, if { a n } is an infinite sequence, then is an infinite series (or simply a series ).

marlo
Download Presentation

One important application of infinite sequences is in representing “infinite summations.”

An Image/Link below is provided (as is) to download presentation 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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Infinite Series One important application of infinite sequences is in representing “infinite summations.” Informally, if {an} is an infinite sequence, then is an infinite series (or simply a series). The numbers a1, a2, a3, are the terms of the series. For some series it is convenient to begin the index at n = 0 (or some other integer). As a typesetting convention, it is common to represent an infinite series as simply Infinite series

  2. Infinite Series In such cases, the starting value for the index must be taken from the context of the statement. To find the sum of an infinite series, consider the following sequence of partial sums. If this sequence of partial sums converges, the series is said to converge.

  3. Infinite Series

  4. Geometric Series In general, the series given by is a geometric series with ratio r. Geometric series

  5. Geometric Series

  6. Geometric Series

  7. nth-Term Test for Divergence The contrapositive of Theorem 9.8 provides a useful test for divergence. This nth-Term Test for Divergence states that if the limit of the nth term of a series does not converge to 0, the series must diverge.

More Related