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.

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]

Clicker Question 3 The series A. converges B. diverges

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?

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…?

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

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