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

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

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.

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

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