1. Calculus II (MAT 146) Dr. Day Monday, April 9, 2018
Series Worth Remembering (11.2)
Your First Tests For Convergence! (11.2, 11.3)
The Divergence Test (11.2)
The Integral Test (11.3)
The p-Series Test (11.3)
Monday, April 9, 2018
MAT 146

2. Fact or Fiction?
(1) If the series 𝑛=1 ∞ 𝑎 𝑛 is convergent, then lim 𝑛→∞ 𝑎 𝑛 =0.
(2) If lim 𝑛→∞ 𝑎 𝑛 =0, then the series 𝑛=1 ∞ 𝑎 𝑛 is convergent.
(3) If lim 𝑛→∞ 𝑎 𝑛 does not exist or if lim 𝑛→∞ 𝑎 𝑛 ≠0, then the series 𝑛=1 ∞ 𝑎 𝑛 is divergent.
Monday, April 9, 2018
MAT 146

3. Notable Series
A geometric series is created from a sequence whose successive terms have a common ratio. When will a geometric series converge?
Monday, April 9, 2018
MAT 146

4. Notable Series
The harmonic series is the sum of all possible unit fractions.
Monday, April 9, 2018
MAT 146

5. Notable Series
A telescoping sum can be compressed into just a few terms.
Monday, April 9, 2018
MAT 146

6. Our first Series Convergence Test
Our first Series Convergence Test The nth-Term Test also called The Divergence Test
If lim 𝑛→∞ 𝑎 𝑛 does not exist or if lim 𝑛→∞ 𝑎 𝑛 ≠0, then the series 𝑛=1 ∞ 𝑎 𝑛 is divergent.
Monday, April 9, 2018
MAT 146

7. Monday, April 9, 2018
MAT 146

8. Monday, April 9, 2018
MAT 146

9. Monday, April 9, 2018
MAT 146

10. Monday, April 9, 2018
MAT 146

12. Monday, April 9, 2018
MAT 146

14. Monday, April 9, 2018
MAT 146

15. Monday, April 9, 2018
MAT 146

16. Monday, April 9, 2018
MAT 146

17. Monday, April 9, 2018
MAT 146

18. Monday, April 9, 2018
MAT 146

19. Monday, April 9, 2018
MAT 146

20. Monday, April 9, 2018
MAT 146