existence of a sequence satisfying two inequalities
Source: Balkan Mathematical Olympiad 2008 Problem 2
May 6, 2008
inequalitiesinductionfunctionCauchy Inequalityinequalities proposed
Problem Statement
Is there a sequence of positive reals satisfying simoultaneously the following inequalities for all positive integers :
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?