12.2.6. Strong Induction

Try these first

1. 1.

   What is the base case in proof by induction?

   Hint

   Think about the starting point of your proof.

2. 2.

   Define regular induction in simple terms.

   Hint

   Remember the one-step assumption.

3. 3.

   What is the first step in a proof by induction?

   • Base Case
   • Inductive Step
   • Conclusion

   Hint

   What do you need to prove first in induction?

4. 4.

   In strong induction, how many prior cases can you use?

   • Only one
   • All prior cases
   • None

   Hint

   Think about how far back can you go in your assumptions.

5. 5.

   Prove by induction that 3^n > n^3 for all n ≥ 4.

   Hint

   What transformation can you apply to connect k and k+1?

6. 6.

   Use both regular and strong induction to show that all integers greater than 1 can be expressed as a product of primes.

   Hint

   Consider the characteristics of prime vs composite numbers.