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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.

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Chapter 9.3

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  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

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