ILL 1987 Problem 75

Let $a_k$ be positive numbers such that $a_1 \geq 1$ and $a_{k+1} -a_k \geq 1 \ (k = 1, 2, . . . )$ . Prove that for every $n \in \mathbb N,$ $$\sum_{k=1}^{1987}\frac{1}{a_{k+1} \sqrt[1987]{a_k}} <1987$$

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