# 2019-17 0.7?

Let $$n \in \mathbb{Z}^+$$ and $$x, y \in \mathbb{R}^+$$ such that $$x^n + y^n = 1$$. Prove that
$(1-x)(1-y) \left( \sum_{k=1}^n \frac{1+x^{2k}}{1+x^{4k}} \right) \left( \sum_{k=1}^n \frac{1+y^{2k}}{1+y^{4k}} \right) < \frac{7}{10}.$

GD Star Rating