Problem #PRU-111805

Problems Calculus Real numbers Integer and fractional parts. Archimedean property Methods Pigeonhole principle Pigeonhole principle (angles and lengths)

13–15 3.0

Problem

The sequence $(a_{n})$ is given by the conditions $a_{1} = 1000000$ , $a_{n + 1} = n ⌊ a_{n} / n ⌋ + n$ . Prove that an infinite subsequence can be found within it, which is an arithmetic progression.

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