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Irish 1990 paper 2 #1

Source: 2nd Irish Mathematical Olympiad

September 7, 2014
inequalities proposedinequalities

Problem Statement

Let n>3n>3 be a natural number . Prove that 133+143+⋯+1n3<112.\frac{1}{3^3}+\frac{1}{4^3}+\cdots+\frac{1}{n^3}<\frac{1}{12}.
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