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Another inequality with distinct positive integers

Source: Romanian IMO Team Selection Test TST 1988, problem 4

October 1, 2005
inequalitiesinductioninequalities proposed

Problem Statement

Prove that for all positive integers 0<a1<a2<⋯<an0<a_1<a_2<\cdots <a_n the following inequality holds: (a1+a2+⋯+an)2≤a13+a23+⋯+an3. (a_1+a_2+\cdots + a_n)^2 \leq a_1^3+a_2^3 + \cdots + a_n^3 . Viorel Vajaitu
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