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Binomial Theorem: Proof by Mathematical Induction

This powerful technique from number theory applied to the Binomial Theorem

Mathematical Induction is a proof technique that allows us to test a theorem for all natural numbers. We’ll apply the technique to the Binomial Theorem show how it works.

The Inductive Process

Figure 1: The inductive process

The inductive process requires 3 steps.

The Base Step

We are making a general statement about all integers. In the base step, we test to see if the theorem is true for one particular integer.

The Inductive Hypothesis

We assume that the theorem is true for some integer, t.

The Inductive Step

We show that if the theorem applies to some integer t, it must also apply to the integer t+1.