Mathematical Induction
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5 Terms
What are the steps for mathematical induction?
Induction: Let n be a natural number and let P(n) be a statement that depends on n
Base step: P(1) is true, and
Inductive step: if P(k) is true, then P(k + 1) is also true.
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 .
