Question

Determinati numerele naturale n care verifica relatiile :{$\frac{1}{9} \ \textless \ \frac{1}{2n+1} \ \textless \ 1$1}{9} < \frac{1}{2n+1} < 1

Answer 1

$\dfrac{1}{9}<\dfrac{1}{2n+1}<1\Big|\verb ^(-1) \\ \\\\\Leftrightarrow\,9 > 2n+1 > 1 \\ \\ \Leftrightarrow\,1 < 2n+1 < 9\Big|-1\\ \\ \Leftrightarrow \,0 < 2n < 8\Big|:2 \\ \\ \Leftrightarrow \,0 < n < 4 \\ \\\\\Rightarrow\,\boxed{n\in \big\{1,2,3\}}$

Answer 2

Explicație pas cu pas:

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