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TOT 285 1991 Spring A J1 product of 99 fractions >2/3

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June 9, 2024
algebrainequalities

Problem Statement

Prove that the product of the 9999 fractions k3−1k3+1  ,      k=2,3,...,100\frac{k^3-1}{k^3+1} \,\, , \,\,\,\,\,\, k=2,3,...,100 is greater than 2/32/3.
(D. Fomin, Leningrad)
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