1994 USAMO Problems/Problem 4
Revision as of 00:40, 12 April 2011 by Zero.destroyer (talk | contribs) (Created page with 'Since each <math>a_{i}</math> is positive, by Muirhead's inequality, <math>2(\sum a_{i}^2) \ge (\sum a)^2 \ge n</math>. Now we claim that <math> \frac{n}{2}> (\frac{1}{4})*(1+..…')
Since each is positive, by Muirhead's inequality,
. Now we claim that
, giving
works, but we set the base case
, which gives
. Now assume that it works for
.
By our assumption, now we must prove that, for
case, which simplifies down to
, which is clearly true for
. So we are done.