Y by
Let
. Suppose that the sequence
satisfies
and
. The sequence
is the nondecreasing permutation of
. Prove that
![\[\sum_{i=1}^n \sum_{j=1}^n (j-i)^2a_ia_j \le \sum_{i=1}^n \sum_{j=1}^n (j-i)^2b_ib_j \]](//latex.artofproblemsolving.com/e/5/9/e598b926b793c06cb1cc5529773e5c278279e59b.png)






![\[\sum_{i=1}^n \sum_{j=1}^n (j-i)^2a_ia_j \le \sum_{i=1}^n \sum_{j=1}^n (j-i)^2b_ib_j \]](http://latex.artofproblemsolving.com/e/5/9/e598b926b793c06cb1cc5529773e5c278279e59b.png)
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