12.2.1. Introduction to Proof by Induction

Try these first

1. 1.

   What is the first step in a proof by induction?

   Hint

   It’s the initial case in the sequence.

2. 2.

   What does the inductive step involve?

   Hint

   It’s about moving one step forward.

3. 3.

   What two components make proof by induction?

   • Base Case and Inductive Step
   • Base Case and Final Step
   • Initial Step and Induction

   Hint

   Think about what structure the proof follows.

4. 4.

   True or False: Strong induction requires proving each previous case independently.

   • True
   • False

   Hint

   Remember the differences in dependencies between both methods.

5. 5.

   Prove by induction that the product of the first n odd numbers is given by n^2.

   Hint

   Look for a pattern or formula involving squares.

6. 6.

   Use strong induction to show that every integer greater than or equal to 12 can be obtained using combinations of 4s and 5s.

   Hint

   Consider several ways to break down k + 1.