What is the Principle of Mathematical Induction?

Conditions

• $P(1)$ is true.
• For any k, $P(k)$ implies $P(k+1)$.
• n is a natural number.

Reasoning, step by step

1. Verify the base case $P(1)$.
2. Prove the inductive step: assume $P(k)$ and show $P(k+1)$.
3. Apply the principle to conclude $P(n)$ is true for all n in N.

Example

The video concludes with a title card: 'THE PRINCIPLE OF MATHEMATICAL INDUCTION'. The narrator states, 'Hence, by the principle of the mathematical induction, we can say that P of n is true for all natural numbers n.'

Common misconceptions

• Thinking the principle applies to real numbers or negative integers without adjustment.
• Believing that proving $P(1)$ and $P(2)$ is sufficient.

Watch the explanation

Explore next

• How is this principle applied to the sum of even integers?
• Why is the inductive step necessary?