olymmath

BALKAN-SL 2008 A2

    Is there a sequence a1,a2,…a_1,a_2,\ldots of positive reals satisfying simoultaneously the following inequalities for all positive integers nn: a) a1+a2+…+an≤n2a_1+a_2+\ldots+a_n\le n^2 b) 1a1+1a2+…+1an≤2008\frac1{a_1}+\frac1{a_2}+\ldots+\frac1{a_n}\le2008?

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