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max of f (x) = \frac{x + x^2 +...+ x^{2n-1}}{(1 + x^n)^2}

Source: Austrian Polish 1991 APMC

May 1, 2020
functionmaxalgebra

Problem Statement

For a given positive integer nn determine the maximum value of the function f(x)=x+x2+...+x2n−1(1+xn)2f (x) = \frac{x + x^2 +...+ x^{2n-1}}{(1 + x^n)^2} over all x≥0x \ge 0 and find all positive xx for which the maximum is attained.
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