Real numbers/Heron/s method/Heron sequence/Definition

Heron sequence

Let ${}c\in \mathbb {R} _{+}$ denote a positive real number. The Heron-sequence, with the positive initial value ${}x_{0}$, is defined recursively by

${}x_{n+1}:={\frac {x_{n}+{\frac {c}{x_{n}}}}{2}}\,$