IMO Shortlist 1981 problem 16
Dodao/la:
arhiva2. travnja 2012. A sequence of real numbers
![u_1, u_2, u_3, \dots](/media/m/0/0/1/00144cdc01efa81b696e2766ba0d3b87.png)
is determined by
![u_1](/media/m/8/3/b/83b3874ea63305cce97f49c8c4ec34ea.png)
and the following recurrence relation for
![n \geq 1](/media/m/a/9/8/a982fcac3e2c9e0d94e965d6efb5a582.png)
:
![4u_{n+1} = \sqrt[3]{ 64u_n + 15.}](/media/m/1/9/4/194c2a01ba0888d4172c43de547cdf43.png)
Describe, with proof, the behavior of
![u_n](/media/m/4/e/f/4ef22a367647acd2e57faa44940d07c1.png)
as
%V0
A sequence of real numbers $u_1, u_2, u_3, \dots$ is determined by $u_1$ and the following recurrence relation for $n \geq 1$:
$$4u_{n+1} = \sqrt[3]{ 64u_n + 15.}$$
Describe, with proof, the behavior of $u_n$ as $n \to \infty.$
Izvor: Međunarodna matematička olimpijada, shortlist 1981