1. 10.4 The Divergence and Integral Test Math 6B Calculus II

2. The Divergence Test

3. Harmonic Series

4. The Integral Test Suppose f is a continuous, positive, decreasing function on and let a k = f (k). Then the series is convergent if and only if the improper integral is convergent.

5. The Integral Test In other words:

6. p - Series Q: Does the series converge? (p is constant) A:It depends on what p is, lets look at p >1, p < 1, p = 1.

7. p - Series

8. Estimating the Sum of a Series

9. Furthermore, the exact value of the series is bounded as follow:

10. Properties of Convergent Series