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

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}