Principles of Analysis

Homework Assignment #11 (LAST Assignment!)

Due Tuesday, Dec. 10, 5:00 pm

Homework should be placed in the MA242 folder outside my office. There are no mulligans allowed for this assignment.

All problem numbers refer to Bilodeau and Thie's book, the required text for the course. You should write up solutions neatly to all problems, paying particular attention to your arguments and proofs. A nonempty subset will be graded. You are strongly encouraged to work on these problems with other classmates, although the solutions you turn in should be your own work.

Section 6.2
Problems:   1 (parts a, b, d, e), 4 (parts a, b, e), 5, 11

Hint: For problem #1e, you may use the inequality ln(n) < n. (How would you prove this?) For problem #11a, apply the nth-term test to the first series in order to bound |a_n b_n|.

Section 6.3
Problems:   1 (parts a, b, c, f), 2a, 7, 9

Hint: For problem #7b, start with the power series expansion for 1/(1-x^2) (it's a geometric series), then integrate both sides. You will need to use partial fractions.