1 / 6

Chapter 9.3

Chapter 9.3. THE INTEGRAL TEST AND p -SERIES. After you finish your HOMEWORK you will be able to…. Use the Integral Test to determine whether an infinite series converges or diverges Use properties of p -series and harmonic series. THEOREM 9.10 THE INTEGRAL TEST.

nigel
Download Presentation

Chapter 9.3

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. Chapter 9.3 THE INTEGRAL TEST AND p-SERIES

  2. After you finish your HOMEWORK you will be able to… • Use the Integral Test to determine whether an infinite series converges or diverges • Use properties of p-series and harmonic series

  3. THEOREM 9.10THE INTEGRAL TEST If f is positive, continuous, and decreasing for and , then and either both converge of both diverge.

  4. p-SERIES AND HARMONIC SERIES The following series is a p-series, where p is a positive constant. A special case of the p-series is called the harmonic series. This occurs when

  5. In music, strings of the same material, diameter, and tension, whose lengths form a harmonic series, produce harmonic tones.

  6. THEOREM 9.11CONVERGENCE OF p-SERIES The p-series 1. Converges if and 2. Diverges if

More Related