University of South Carolina High School Math Contest/1993 Exam/Problem 22
Problem
Let
and
Then which of the following inequalities is true?
Solution
If you imagine expanding out the expression for , you can see that every term in will appear once, along with plenty of others. (Think of the prime factorizations and you can figure out which products give the terms of .) Since all terms are positive, .
so .
Putting these two facts together, .