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on n^6+5n^5*sin(n)+1

Source: France 1988 P2

May 18, 2021
algebra

Problem Statement

For each n∈Nn\in\mathbb N, determine the sign of n6+5n5sin⁡n+1n^6+5n^5\sin n+1. For which n∈Nn\in\mathbb N does it hold that n2+5ncos⁡n+1n6+5n5sin⁡n+1≥10−4\frac{n^2+5n\cos n+1}{n^6+5n^5\sin n+1}\ge10^{-4}.
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