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

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_n  = ((3(√3))/π)