Here, the speed at which a convergent sequence approaches its limit is called the rate of convergence. This concept is of practical importance if we deal with a sequence of successive approximations for an iterative method, as then typically fewer iterations are needed to yield a useful approximation if the rate of convergence is higher.

**Convergence of A Sequence**

A sequence *α* if for every *α* is called the limit of the sequence and we sometimes write

**Convergence speed for iterative methods**

Let *α* with order *q* if

where *μ* is called the rate of converegence.

Particularly, if