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a+1/a-2

Source: 3-rd Hungary-Israel Binational Mathematical Competition 1992

May 24, 2007
inequalitiesinductionfunctioninequalities proposed

Problem Statement

Prove that if cc is a positive number distinct from 11 and nn a positive integer, then n2≤cn+c−n−2c+c−1−2.n^{2}\leq \frac{c^{n}+c^{-n}-2}{c+c^{-1}-2}.
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