# Let n be a natural number. Find all real numbers x satisfying the equation ∑ k ∈ [k = 1, n] kx^k/1+x^2k = n(n+1)/4

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Let n be a natural number. Find all real numbers x satisfying the equation

∑ k ∈ [k = 1, n] kxk/1+x2k = n(n+1)/4

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Inequality holds as all terms of the summation are not of the same sign for k > 1 & for k = 1, LHS is negative. Hence only solution is x = 1.