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To iterate is to perform the same procedure over and over again. Sometimes we can solve equations approximately by iteration, for example:

x2 + x = 5 ⇒ x = √   5− x   , so, let xn = √   5− xn−1

Then, if we take as our first guess x₀=1, we get:

x1 = 2 x2 = 1.7320508 x3 = 1.807747 x4 = 1.7866877 :

The exact answer is about 1.7912878.