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# Chapter 9.3 - PowerPoint PPT Presentation

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

THE INTEGRAL TEST AND

p-SERIES

• Use the Integral Test to determine whether an infinite series converges or diverges

• Use properties of p-series and harmonic series

THEOREM 9.10THE INTEGRAL TEST

If f is positive, continuous, and decreasing for and , then

and

either both converge of both diverge.

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

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

THEOREM 9.11 tension, whose lengths form a harmonic series, produce harmonic tones. CONVERGENCE OF p-SERIES

The p-series

1. Converges if and

2. Diverges if