-4
$\begingroup$

Possible Duplicate:
How to prove that this sequence converges?

Let the sequence defined recursively by the equation: $ a_n = a_{a_{n - 1} } + a_{n - a_{n - 1} } $ How can I prove that $ \mathop {\lim }\limits_{n \to \infty } \frac{{a_n }} {n} $

EDIT: $ a_0 = a_1 = 1 $ Thanks

  • 0
    I download it , thx2011-09-14

1 Answers 1

3

If you calculate the first few terms of the sequence, you should very easily be able to conjecture a closed form for $a_n$ that works for all $n>0$. Proving the conjecture is an easy exercise in mathematical induction. And once you have that, the value of the limit is obvious.