CSCE 235
Homework
Assignment 6
Assigned: February 27, 2008
Due: 12:30 p.m. March 5,
2008
(Homework 5
minutes late will not be accepted)
1. (10 points) Prove by induction that
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 
whenever n is a
positive integer.
6. (10 points) Prove by induction that 
whenever n is a
positive integer greater than 6.
7. (10 points) Prove by induction that all numbers of
the form 
are divisible by 7 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).