# strange recurrence relation and limit

$$a_{n+1}=\frac{a_n+b_n}{2}$$

$$b_{n+1}=\sqrt{a_{n+1}b_{n}}$$

also, $$a_1=a$$ and $$b_1=b$$

can someone find $$\lim_{n\to\infty}a_{n}$$ This question is from guillaume musso's novel. I remember that the answer included $$\arccos$$ thing..

• Which novel, by the way? – J.G. Mar 12 at 17:52
• @J.G. La Jeune Fille et la Nuit – scitamehtam Mar 13 at 16:56