# Definition of convergent

Definition of convergent
1. convergent Adjective That converges or focuses
2. convergent Adjective A sequence x_n in a metric space with metric "d" is convergent to a point x^* , denoted as x_n \rightarrow x^* , if for every \epsilon > 0 there is a natural number "N" such that for every k \ge N : d(x_k, x^*) < \epsilon.
3. convergent Noun the rational number obtained when a continued fraction has been terminated after a finite number of terms