1. Testing Infinite Series – Summary 11/30/12
Do individual terms go to 0? If no, divergence! If yes, go on.
Is the series geometric with first term a and ratio r? If so and if |r|  1, divergence!. Otherwise, convergence and answer is a / (1 - r).
Can the series be compared to:
An integrable function? If so, it will converge or diverge exactly when the corresponding improper integral converges or diverges.
Another series whose behavior we already know?

2. Testing (Continued)
Do the terms alternate sign? If so (and if terms are going to 0, of course), convergence.
Look at the limit of the ratio of the absolute values of (n+1)st term to the nth term as n goes to infinity. If that limit is less than 1, absolute convergence. Greater than 1? Divergence. Equals 1? Test Fails.

3. Clicker Question 1 The series A. converges absolutely.
B. converges conditionally but not absolutely.
C. diverges.

4. Clicker Question 2 The series A. converges absolutely.
B. converges conditionally but not absolutely.
C. diverges.

5. Clicker Question 3 The series A. converges absolutely.
B. converges conditionally but not absolutely.
C. diverges.

6. Assignment for Monday
Work on Hand-in #3, which is due on Tuesday, Dec 4, at 5 pm.