If , and for all ,…

MATHEMATICS · Subjective · A Level · Mathematics · Numerical methods · Numerical methods

Problem

f(n+1) = \frac{1}{2} \left\{ f(n) + \frac{9}{f(n)} \right\}

n \in \mathbb{N}

and

f(n) > 0

for all

n \in \mathbb{N}

, then

\lim_{n \rightarrow \infty} f(n) = ?