8: Proof By Induction

Question 1

What are the 4 steps of P.B.I.?

Answer 1

1: Basis
2. Assumption
3. Inductive
4. Conclusion

Question 2

Recite the conclusion step of P.B.I. for sums.

Answer 2

If the summation formula is true for n=k then it is shown to be true for n=k+1. As the result is true for n=1, it is also now true for all nEZ+ by mathematical induction.

Question 3

Recite the conclusion step of P.B.I. for divisibility sets.

Answer 3

If f(n) is divisible by {n} when n=k, then it has been shown that f(n) is divisible by {n} when n=k+1. As f(n) is divisible by {n} when n=1, f(n) is also divisible by 4 for all nEZ+ by mathematical induction.

Question 4

Recite the conclusion step of P.B.I. for matrices.

Answer 4

If the matrix equation is true for n=k, then it is shown to be true for n=k+1. As the matrix equation is true for n=1, it is also true for all nEZ+ by mathematical induction.