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My mentor tommy1729 told me :
Let $b_1 = 1.$
Let $ b_2 = x.$
Also $ \frac{1}{2} < x < 2 $
Define for $ n>2 $:
$$ b_n = \frac{\exp(\ln(b_{n-1})^3)}{b_{n-2}} $$
Then
$$ \sup_{n>2} b_n = x , \inf_{n>2} b_n = \frac{1}{x} $$
Is this true ?
How to show that ?
We can rewrite the sequence $b_n$ ...
