12.2.2. Argument Form of Induction Proof

Try these first

1. 1.

   What does the base case in induction verify?

   Hint

   Think about the beginning of the sequence.

2. 2.

   Define the inductive step.

   Hint

   What follows after proving the base case?

3. 3.

   What is the purpose of the base case in induction?

   • To prove the statement is true for k
   • To establish the foundation of the proof
   • To generalize the statement

   Hint

   Think about why we start with a specific case.

4. 4.

   True or False: Strong induction requires proving a base case.

   • True
   • False

   Hint

   Reflect on what's necessary in any induction proof.

5. 5.

   Suppose you're asked to prove the sum of the first n odd numbers is n^2 using induction. Outline your proof.

   Hint

   Consider how the next odd number relates to your inductive assumption.

6. 6.

   Prove that for all integers n ≥ 1, 2^n > n^2. Discuss the base case and find the value of n for which this holds true.

   Hint

   How does the exponential function compare to polynomials as n grows?