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第13届普特南数学竞赛的A—1题为2n3n∑nk=1k4n+36n1文[1]利用Abel变换改进不等式为 2n+13n≤∑nk=1k≤4n+36n-162文[2]进一步改进为 2n+23-2-13≤∑nk=1k≤4n+36n-163本文将探讨比3式更强的不等式.定理 对任意正整数n,有 4n+36n+124n-524≤∑nk=1k≤4n+36n-164当且仅当n
The 13th Putnam mathematics competition A-1 titled 2n3n∑nk=1k4n+36n1 text [1] The improved inequality using Abel transformation is 2n+13n≤∑nk=1k≤4n+36n-162[2] further The improvement is 2n+23-2-13≤∑nk=1k≤4n+36n-163. In this paper we will discuss stronger inequalities than 3. Theorem For any positive integer n, there are 4n+36n+124n-524≤∑nk= 1k≤4n+36n-164 if and only if n