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.
THE INTEGRAL TEST AND
If f is positive, continuous, and decreasing for and , then
either both converge of both diverge.
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.
1. Converges if and
2. Diverges if