## Math 417 Homework 5: Due Friday February 21

Instructions: You can discuss these problems with others, but write up your solutions on your own (i.e., don't just copy someone else's solutions, else the feedback I give you won't help you much). Please be neat and write in full sentences.
Do three of the last four problems, and one of the first three.
• [1] Problem #24 on p. 24. (Hint: see Example 10 on p. 16.)

• [2] Let {f1, f2, f3, ...} be a sequence of integers such that f1 > 1 and for n > 1 such that fn > 3fn - 1 + 2. Use induction to prove that fn > 3n/2 - 1 for every integer n > 0. (Indicate which form of induction you used; Theorem 0.4 or 0.5.)

• [3] Let {f0, f1, f2, f3, ...} be a sequence of integers such that 1 < f0 < f1 and for n > 1 such that fn + 1 > fn + fn - 1. Use induction to prove that fn > 1.6n for every integer n > -1. (Indicate which form of induction you used; Theorem 0.4 or 0.5.)

• [4] Problem 40 on p. 84.

• [5] Problem 54 on p. 85.

• [6] Problem 4 on p. 111.

• [7] Problem 8 on p. 111.