# Computing The Arithmetic-Harmonic Mean

Calculus Level 3

Define two sequences $$\{a_n\}$$ and $$\{b_n\}$$ by the recursive system: $$a_0 = 4$$, $$b_0 = 25$$, $a_{n+1} = \frac{a_n + b_n}{2}$ $b_{n+1} = \frac{2}{\frac{1}{a_n} + \frac{1}{b_n}}$ What is $$\displaystyle \lim_{n\to\infty} a_n$$?

×