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

1989 USAMO Problems/Problem 5

Revision as of 16:41, 16 October 2007 by 1=2 (talk | contribs) (New page: ==Problem== Let <math>u</math> and <math>v</math> be real numbers such that <math> (u + u^2 + u^3 + \cdots + u^8) + 10u^9 = (v + v^2 + v^3 + \cdots + v^{10}) + 10v^{11} = 8. </math> Det...)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Let $u$ and $v$ be real numbers such that

$(u + u^2 + u^3 + \cdots + u^8) + 10u^9 = (v + v^2 + v^3 + \cdots + v^{10}) + 10v^{11} = 8.$

Determine, with proof, which of the two numbers, $u$ or $v$, is larger.

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See Also

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1989_USAMO_Problems/Problem_5&oldid=18201"