1 / 16

Sec. 9.3: The Integral Test and p -Series

Sec. 9.3: The Integral Test and p -Series. Sec. 9.3: The Integral Test and p -Series. The Integral Test can be applied only to series with positive terms. Sec. 9.3: The Integral Test and p -Series. Remainder: 0 < R N <. converges. diverges.

kagami
Download Presentation

Sec. 9.3: The Integral Test and p -Series

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. Sec. 9.3: The Integral Test and p-Series

  2. Sec. 9.3: The Integral Test and p-Series The Integral Test can be applied only to series with positive terms.

  3. Sec. 9.3: The Integral Test and p-Series Remainder: 0 < RN < converges diverges

  4. Sec. 9.3: The Integral Test and p-Series Ex: Apply the Integral Test to the following. Is an decreasing? Yes Decreasing for x≥ 1.

  5. Sec. 9.3: The Integral Test and p-Series Ex: Apply the Integral Test to the following.

  6. Sec. 9.3: The Integral Test and p-Series Ex: Apply the Integral Test to the following. Is an decreasing? Yes Decreasing for x≥ 1.

  7. Sec. 9.3: The Integral Test and p-Series Ex: Apply the Integral Test to the following. NOTE: The sum of the series is NOT the value of the integral !!!

  8. Sec. 9.3: The Integral Test and p-Series p-Series and Harmonic Series A series of the form is a p-series, where p is a positive constant.

  9. Sec. 9.3: The Integral Test and p-Series p-Series and Harmonic Series When p = 1, is the harmonic series.

  10. Sec. 9.3: The Integral Test and p-Series p-Series and Harmonic Series The general harmonic series is of the form

  11. Sec. 9.3: The Integral Test and p-Series p-Series and Harmonic Series The Integral Test is used to establish the convergence / divergence of p-series.

  12. Sec. 9.3: The Integral Test and p-Series p> 1 p≤ 1

  13. Sec. 9.3: The Integral Test and p-Series Ex: Determine the convergence / divergence of the following. State these. p = 1, p≤ 1 p = 2, p> 1

  14. Sec. 9.3: The Integral Test and p-Series Ex: Determine the convergence / divergence of the following. Telescoping series? No No Geometric series? No p-series? Series to use nth-Term Test? Try the Integral Test.

  15. Sec. 9.3: The Integral Test and p-Series Ex: Determine the convergence / divergence of the following. Yes Σ decreasing? Yes

  16. Sec. 9.3: The Integral Test and p-Series Ex: Determine the convergence / divergence of the following.

More Related