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
- Prove that for all .
- Prove that for all .
- Prove that is divisible by 2 for all .
- Prove that .