If $$n \in N^+ $$ , prove
$$
\dfrac{1}{2}\leq\dfrac{1}{n+1}+\dfrac{1}{n+2}+\dots+\dfrac{1}{2n}

Question

If $$n \in N^+ $$  , prove 
$$
\dfrac{1}{2}\leq\dfrac{1}{n+1}+\dfrac{1}{n+2}+\dots+\dfrac{1}{2n}<1 $$

Uniteasy Admin · Accepted Answer

$$ \because n < n+k <2n $$
$$ 	herefore \dfrac{1}{2n} <\dfrac{1}{n+k}<\dfrac{1}{n} $$