Solution Found!
Use the principle of mathematical induction to show that
Chapter 5, Problem 83E(choose chapter or problem)
Problem 83E
Use the principle of mathematical induction to show that P(n) is true for n = b, b + 1, b + 2,…, where b is an integer, if P(b) is true and the conditional statement P(k) → P(k + 1) is true for all integers k with k ≥ b.
Questions & Answers
QUESTION:
Problem 83E
Use the principle of mathematical induction to show that P(n) is true for n = b, b + 1, b + 2,…, where b is an integer, if P(b) is true and the conditional statement P(k) → P(k + 1) is true for all integers k with k ≥ b.
ANSWER:
Step 1 of 3
The principle of mathematical induction proves a statement by the following two steps.
1. Basis step
2. Inductive step.
Basis step: This step proves that the statement is true for the basic value.
Inductive step: This includes the assumption of the inductive hypothesis and its proof.
We have to prove if P(b) is true, and the conditional statement P (k) ? P (k + 1) is true, then P(n) is true for n=b,b+1,b+2... .