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Sequence

Source: APMO 1995

March 11, 2006
algebra unsolvedalgebra

Problem Statement

Determine all sequences of real numbers a1a_1, a2a_2, …\ldots, a1995a_{1995} which satisfy: 2\sqrt{a_n - (n - 1)} \geq a_{n+1} - (n - 1), \ \mbox{for} \ n = 1, 2, \ldots 1994, and 2a1995−1994≥a1+1. 2\sqrt{a_{1995} - 1994} \geq a_1 + 1.
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