1. Clicker Question 1
The shortest interval which the Integral Test guarantees us will contain the value of is:
A. 0 to 1
B. 0 to ½
C. ½ to 1
D. ½ to 5/8
E. The series diverges.

2. Clicker Question 2
The shortest interval which the above result guarantees us will contain the value of 1/(1 + n2) is:
A. [0, 2]
B. [0, /2]
C. [/4, 1]
D. [/4, /4 + ½]
E. [/4, /4 + 1]

3. Clicker Question 3
The series
A. converges
B. diverges

4. Alternating Series (11/20/13)
If the terms of a series alternate sign and if the terms themselves are approaching 0, then the series converges.
Example: 1 – 1/2 + 1/3 - 1/4 + 1/5 - … must converge! (Guess the name of this series.)
To what, you ask? Not obvious, since this series is not geometric. Experiment a bit?

5. The Alternating Series Test
Theorem. If b1  b2  b3 … is a decreasing sequence of positive numbers and if limnbn = 0, then the series (-1)(n+1)bn converges.
Proof outline:
The even partial sums s2n are monotone increasing and bounded above by b1, so…?
Each odd partial sum s2n+1 = s2n + bn+1 , so…?

6. Clicker Question 4 The series A. converges to a number smaller than 0
B. converges to a number smaller than 3
C. converges to a number bigger than 3
D. diverges

7. Assignment for Friday
Read Section 11.5 to the bottom of page 729 and do Exercises 1 – 13 odd, 32, 33, and 35.