To now the real sequence in the follwing image : a_1 =1 ,a_2 =2 a_(nk +1) = ((a_(2k−1) +a_(2k) )/2) ∀ k ∈ Z^+ a_(2k+2) = (√(a_(2k) a_(2k+1) )) then prove that : lim_(n→∞) a


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Question Number 105130 by 175mohamed last updated on 26/Jul/20

$T o n o w t h e r e a l s e q u e n c e i n t h e$ $f o l l w i n g i m a g e :$ $a_{1} = 1, a_{2} = 2$ $a_{n k + 1} = \frac{a_{2 k - 1} + a_{2 k}}{2} \forall k \in Z^{+}$ $a_{2 k + 2} = \sqrt{a_{2 k} a_{2 k + 1}}$ $t h e n$ $p r o v e t h a t : \lim_{n \to \infty} a_{n} = \frac{3 \sqrt{3}}{π}$
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