1. THE INTEGRAL TEST AND p-SERIES
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 9.10 THE 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 9.11 CONVERGENCE OF p-SERIES
The p-series
1. Converges if and
2. Diverges if