Mathematical Induction

What are the steps for mathematical induction?

1. Induction: Let n be a natural number and let P(n) be a statement that depends on n

2. Base step: P(1) is true, and

3. Inductive step: if P(k) is true, then P(k + 1) is also true.

4. Then P(n) is true for all n ≥ 1 .

What is the induction?

Let P(n) be the statement … where P(n) is the algebraic equation that we are trying to prove

What is the base step?

Let n = 1. Notice that sub in 1 into the equation so that P(1) is true.

What is the inductive step?

Let k be a natural number and assume that P(k) is true, so that sub k into equation. We want to show that P(k + 1) is true. Notice that by the inductive hypothesis, sub k + 1 into equation so that P(k + 1) is true

How do you conclude?

Hence by the Principle of Mathematical Induction, P(n) is true for all n ∈ N .