Convergents

Convergents[list] gives a list of the convergents corresponding to the continued fraction terms list.

Convergents[x, n] gives the first n convergents for a number x.

Convergents[x] gives if possible all convergents leading to the number x.

Examples

Convergents from continued fraction terms:

Convergents[{3, 7, 15, 1, 292}]
(* {3, 22/7, 333/106, 355/113, 103993/33102} *)

Convergents of Pi:

Convergents[Pi, 5]
(* {3, 22/7, 333/106, 355/113, 103993/33102} *)

Please visit the official Wolfram Language Reference for more details.