Sect. 9-D Comparison Tests

1. Sect. 9-D Comparison Tests

2. The Direct comparison Test If 0 < an < bnfor all n and positive terms, then: If the larger series converges, then the smaller series must also converge. If the smaller series diverges then the larger series must also diverge

3. The Direct comparison Test Given a series Compare with a similar Geometric or p- Series When choosing a series for comparison you can disregard all but the highest power in the numerator and denominator When choosing an appropriate p-series, you must choose one with the same nth term

4. 1. Does converge or diverge?

5. 2. Does converge or diverge?

6. 3. Does converge or diverge?

7. 4. Does converge or diverge?

8. The Limit comparison Test If an >0, and bn> 0 for all n , then: Where L is finite and positive, then both converge or they both diverge Works well when comparing a messy algebraic series to a p-series or geometric series

9. 5. Does converge or diverge?

10. 6. Does converge or diverge?

11. 7. Does converge or diverge?

12. Home Work Page 630 # 3,4,5,8,9,10,11,14,15,17,19,21,29-35 all