IB Math HL – Lesson 9AB
Mathematical Induction Day 1
Name: ________________________________
Ex1) By examining the cases n = 1, 2, 3, 4, make a conjecture about the sum of
1
1
1
1
1
Sn 



 ... 
1 2 2  3 3  4 4  5
n(n  1)
When we make an informed conjecture about something, we induce a statement or conclusion. From this, we get the
idea of mathematical induction. But the principle of mathematical induction has two formal steps.
Ex2) Prove that 4 n  2 is divisible by 3 for n  Z , n  0 by using induction.
Steps for Proof by Mathematical Induction
Ex3) Prove that n(n 2  5) is divisible by 6 for all n  Z  .
n
Ex4) Prove that
1
n
 (3i  1)(3i  2)  6n  4
i 1
for all n  Z  .
Ex5) A sequence is defined by u1  1 and u n1  2u n  1 for all n  Z  . Prove that u n  2 n  1 for all n  Z 
Homework:
Exercise 9A: #2all
Exercise 9B.1: #2b, 3a
Exercise 9B.2: #1bd