CSC 400 Discrete Structures for Computer Science
Homework #3
Due: 2/3 (Sun)

Revised 1/30

There are two sets of problems in this homework. Do BOTH of them.

General questions

Prove by induction that 1∙2 + 2∙3 + 3∙4 + .. + n∙(n+1) = [n∙(n+1)∙(n+2)] / 3.
Prove by induction that 3n < n! if n is an integer greater than 6.
Prove by induction that 4 + 8 + 12 + .. + 4n = 2n² + 2n, for all n >= 1.
(Note: You must use induction, no other method.)

Textbook questions

Section 4.3 (p. 177-)
13, 28
Section 4.6 (p. 205-)
4

Section 5.1 (p. 242-)
4, 7, 13

Section 5.2 (p. 256-)
11, 12

Section 5.3 (p. 266-)
7

[Extra Credit] Some extra credit will be given if you solve these questions.

Section 2.3 (p.61-)
40, 44