IMO Shortlist 2004 problem A2
Kvaliteta:
Avg: 4,5Težina:
Avg: 6,0 Let
,
,
, ... be an infinite sequence of real numbers satisfying the equation
for all
, where
and
are two different positive reals.
Can this sequence
,
,
, ... be bounded?
Remark This one is from the IMO Shortlist 2004, but it's already published on the official BWM website und thus I take the freedom to post it here:
![a_0](/media/m/6/1/1/61182666f636aa197c5d27a9b3376b53.png)
![a_1](/media/m/6/1/7/6173ac27c63013385bea9def9ff2b61e.png)
![a_2](/media/m/4/0/1/401f4cdfec59fba73ae32fa6769c72cb.png)
![a_n=\left|a_{n+1}-a_{n+2}\right|](/media/m/4/3/d/43d5053911ed895dc573c0e77d2d45ec.png)
![n\geq 0](/media/m/7/c/9/7c9155fe4dfe8430a262cb6a8e30f32f.png)
![a_0](/media/m/6/1/1/61182666f636aa197c5d27a9b3376b53.png)
![a_1](/media/m/6/1/7/6173ac27c63013385bea9def9ff2b61e.png)
Can this sequence
![a_0](/media/m/6/1/1/61182666f636aa197c5d27a9b3376b53.png)
![a_1](/media/m/6/1/7/6173ac27c63013385bea9def9ff2b61e.png)
![a_2](/media/m/4/0/1/401f4cdfec59fba73ae32fa6769c72cb.png)
Remark This one is from the IMO Shortlist 2004, but it's already published on the official BWM website und thus I take the freedom to post it here:
Izvor: Međunarodna matematička olimpijada, shortlist 2004