MATHEMATICAL INDUCTION
MIDWESTERN STATE UNIVERSITY
DR. RANETTE HALVERSON
WHY THE DROPLET TEMPLATE???
Because Mathematical induction makes most
students cry!
Will try to make it painless.
PRINCIPLE OF MATHEMATICAL INDUCTION
Let S(n) be a statement involving an integer n.
Suppose that, for some fixed integer n0,
a) S(n0) is true (i.e. S(n) is true if n = n0 )
b) When integer k >= n0 & S(k) is true, then S(k+1) is true
The S(n) is true for all integers n >= n0
EXAMPLE
S(n): 1 + 2 + 3 +… + n = (n (n + 1)) / 2
• n=4  (4*5)/2 = 10
• n=5  (5*6)/2 = 15
• n=10  (10 * 11)/2 = 55
• n=100  (100*101)/2 = 5050
INDUCTION SAYS….
S(n): 1 + 2 + 3 +… + n = (n (n + 1)) / 2
a) Show that S(n) is true for some (small) integer k
a)
That means it is true at least sometimes!
b) Since S(n) is true for some integer k, show it is also
true for k+1
a)
That means it is true for all integers >= k
HOMEWORK
• Page 84 – Problems 11 & 13