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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.

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Sec. 9.3: The Integral Test and p -Series

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  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.

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