CSCE 235

Homework Assignment 6

Assigned: February 25, 2009

Due: 12:30 p.m. March 4, 2009

(Homework 5 minutes late will not be accepted)

1. (10 points) Prove by induction that the following is true for :

2. (10 points) Prove by induction that

for all .

3. (10 points) Prove by induction that for all .

4. (10 points) Prove by induction that for all .

5. (10 points) Prove by induction that for all .

6. (10 points) Prove by induction that whenever n is a positive integer.

7. (10 points) Prove by induction that all numbers of the form are divisible by 5 for all .

8. (10 points) The product of n elements is denoted . Let x be a real number, . Prove by induction that

for any integer .

Problems based on (Rosen 2003, Gossett 2003, Hein 2002, Goodaire and Parmenter 2002, Ross and Wright 1988).