Iteration Method

The iteration method is a "brute force" method of solving a recurrence relation.  The general idea is to iteratively substitute the value of the recurrent part of the equation until a pattern (usually a summation) is noticed, at which point the summation can be used to evaluate the recurrence.

Of course that all sounds like a legal document, so the best way to understand the iteration method is probably to do a few examples:

Here's another type of recurrence relation:

Now try the practice problems to get the hang of it!