CS 1050 B: Constructing Proofs January 29, 2009
Homework 3
Lecturer: Sasha Boldyreva Due: February 3, 2009
Problem 3.1, 10 points. Let a1= 2, a2= 9, and an= 2an−1+ 3an−2for n≥3. Use
strong induction (the Second Principle of Mathematical Induction) to show that an≤3n
for all positive integers n.
Problem 3.2, 7 points. Problem 14 from Section 4.2 of Rosen’s textbook.
Problem 3.3, 7 points. Problem 32 from Section 4.2 of Rosen’s textbook.
Problem 3.4, 10 points. Problem 38 from Section 4.4 of Rosen’s textbook.
Problem 3.5, 20 points. Problem 18a from Section 7.3 of Rosen’s textbook.