How do I show that this inequality holds for all $x \in (0, 1)$ and $n \in \Bbb N$?
$$ (1-x)^n<\frac{1}{1+nx}.$$
How do I show that this inequality holds for all $x \in (0, 1)$ and $n \in \Bbb N$?
$$ (1-x)^n<\frac{1}{1+nx}.$$
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