Tricki

## Revision of Induction front page from Fri, 24/04/2009 - 20:37

### Example 1: A simple arithmetic identity

Consider the identity

Since the left-hand side of (1) is neither an arithmetic nor a geometric progression, we are unable to use the standard formulas for calculating such sums; and, indeed, it is not obvious how to transform the expression into one that can be manipulated into a formula for the sum. However, this can be proved using induction.

### Induction on a general ordered set

Strengthen your inductive hypothesis Transfinite induction is discussed in a separate article.