Practice Mathematical Induction in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Mathematical induction proves statements indexed by integers by verifying a base case and an inductive step.
Like dominoes: first one falls, and each one knocks over the next.
Example 1
mediumUse mathematical induction to prove: 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}{2} for all n \ge 1.
Example 2
hardProve by induction: n! > 2^n for all integers n \ge 4.
Example 3
mediumProve by induction: 1^2 + 2^2 + 3^2 + \cdots + n^2 = \frac{n(n+1)(2n+1)}{6} for all n \ge 1.
Example 4
mediumProve by induction that 2 + 4 + 6 + \cdots + 2n = n(n+1) for all n \ge 1.