Induction Quiz
MI-4
Name:____________________
NO CALCULATOR.
Show all Work.
6 pts
1. Use Mathematical Induction to show that:
1
1
1



1 2 2  3 3  4
all positive integers n.
6 pts
2. Use Pascal’s Triangle to write out the expansion of each binomial:
a. ( x  y)9
b. ( x  2 y)4

1
n
for

n(n  1) n  1
3 pts
3. Evaluate the sum:
6
5
1
4
2
3
3
2
4
1
5
3
3 1
3 1
3 1
3 1
3 1 1
   6       15       20       15       6        
2
2 2
2 2
2 2
2 2
2 2 2
6
3 pts
4. Determine the coefficient of x 9 in the expansion of ( x  2)12 .
3 pts
5. In the Tower of Hanoi game, clearly explain how to move three disks from one
spindle to one of the other two spindles. What is the minimum number of
moves required to complete this task?
6 pts
 4 if n  1
6. Let an  
. Using Mathematical Induction prove that for all n
 3  an1 if n  2
an  3n  1 .
,