Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

1985 IMO Problems/Problem 6

Revision as of 09:54, 25 July 2012 by DAFR (talk | contribs) (Created page with "For every real number <math>x_1</math>, construct the sequence <math>x_1,x_2,\ldots</math> by setting <math>x_{n+1}=x_n \left(x_n + \frac{1}{n}\right)</math> for each <math>n \ge...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

For every real number $x_1$, construct the sequence $x_1,x_2,\ldots$ by setting $x_{n+1}=x_n \left(x_n + \frac{1}{n}\right)$ for each $n \geq 1$. Prove that there exists exactly one value of $x_1$ for which $0<x_n<x_{n+1}<1$ for every $n$.

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1985_IMO_Problems/Problem_6&oldid=47740"