1. Warm Up

2. Tests for Convergence: The Integral and P-series Tests

3. The Integral Test If f is positive, continuous, and decreasing for x > 1 and a n = f(n), then and Either both converge or diverge.

4. Ex 1:

5. Ex 2:

6. The p-series test The p-series Converges if p >1 Diverges if 0 < p < 1 Test cannot be used if p < 0

7. Ex 3: This is known as the HARMONIC series. The harmonic series DIVERGES.

8. Ex 4:

9. Ex 5:

10. Ex 7:

11. Ex 6:

13. Mixed Practice Mixed Practice Determine whether each series converges or diverges. If it converges and is possible to tell, determine what number it converges to. 1. 2. 3. 4. 5. 6.