2

Part of 2008 Balkan MO

Problems(1)

existence of a sequence satisfying two inequalities

Source: Balkan Mathematical Olympiad 2008 Problem 2

Is there a sequence

a_1,a_2,\ldots

of positive reals satisfying simoultaneously the following inequalities for all positive integers

n

: a) a_1\plus{}a_2\plus{}\ldots\plus{}a_n\le n^2 b) \frac1{a_1}\plus{}\frac1{a_2}\plus{}\ldots\plus{}\frac1{a_n}\le2008?

inequalitiesinductionfunctionCauchy Inequalityinequalities proposed