IMO 2006 Shortlist A2
The sequence of real numbers a0,a1,a2,... is defined recursively by a0 = −1, n X k=0 an−k k + 1 = 0 for n ≥ 1. Show that...
Category: Algebra
Problem
The sequence of real numbers a0,a1,a2,... is defined recursively by a0 = −1, n X k=0 an−k k + 1 = 0 for n ≥ 1. Show that an > 0 for n ≥ 1. (Poland)