Induction

• How to Use Induction in a Proof About Prime Numbers
  See how strong induction proves every integer greater than 1 has a prime factorization, and why induction over prime numbers alone needs care.
• Proof That Every Integer Greater Than 1 Is a Product of Primes
  A strong-induction proof shows every integer greater than 1 is a finite product of primes; handle 1, zero, and negative integers separately.
• How to Prove the Sum of the First n Odd Numbers by Induction
  Prove by induction that the first n odd numbers sum to n squared: verify the base case, then add the next odd number.
• Why Does a Polygon Have the Same Number of Vertices and Sides?
  A polygon has the same number of vertices and sides because each side joins consecutive vertices in one closed cycle.
• What Is a Closed-Form Summation? A Worked Example
  Learn what a closed-form summation means and how to derive and verify one, using the sum of the first n positive integers as a worked example.