Applications of Mathematical Induction

Mathematical induction has many applications beyond proving simple summation formulas. It can be used for inequalities, divisibility, and more complex identities.

Inequality Proofs

Example: Proving an Inequality

Divisibility Proofs

Example: Divisibility by 7

Product Formulas

Example: Product of Terms

Geometric Progression Sum

Example: Proving Geometric Sum

Practice Problems

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