Real numbers/Heron's method/Convergence/Exercise

Let ${}a\in \mathbb {R}$ be a non-negative real number and ${}c\in \mathbb {R} _{+}$. Prove that the sequence defined recursively as ${}x_{0}=c$ and

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

converges to ${}{\sqrt {a}}$.

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