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KöMaL 2020 C1634

    Prove the following inequality: 14+128+170+⋯+1(3k−2)(3k+1)+⋯+12017⋅2020<13.\frac{1}{4} +\frac{1}{28} +\frac{1}{70} +\cdots +\frac{1}{(3k-2)(3k+1)} +\cdots +\frac{1}{2017\cdot 2020} < \frac{1}{3}.

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