# slightly different from AGM

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

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

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

evaluate $$\lim_{n\to\infty}a_{n}$$ This question is from guillaume musso's novel La Jeune Fille et la Nuit . I remember that the answer included $$\arccos$$ thing..I asked this question few days ago but didn't get satisfactory answer. Please help me.

• Is this correct $b_{n+1}=\sqrt{a_{n+1}b_{n}}$? Or is it $b_{n+1}=\sqrt{a_{n}b_{n}}$ – Maria Mazur Mar 13 at 17:07
• @MariaMazur I said it's different from agm because of that. So I'm confused. – scitamehtam Mar 13 at 17:10