IMO 1986 LL AUS1

Let k be one of the integers 2, 3, 4 and let n = 2k −1. Prove

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IMO 1986 LL AUS1

Origin: AUS

Problem

Let k be one of the integers 2, 3, 4 and let n = 2k −1. Prove the inequality 1 + bk + b2k + \cdot \cdot \cdot + bnk \geq(1 + bn)k for all real b \geq0.