Principle of Mathematical Induction

Mathematical induction is a powerful technique for proving statements about natural numbers. It is based on the well-ordering principle of natural numbers.

The Principle

Steps for Mathematical Induction

Example 1: Sum of First Natural Numbers

Example 2: Sum of Squares

Example 3: Divisibility

Practice Problems

1. Prove that for all .
2. Prove that for all .
3. Prove that is divisible by 2 for all .
4. Prove that .