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.

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... .