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

Question

If n \in N^+ $$ , prove

\dfrac{1}{2}\leq \dfrac{1}{n+1}+\dfrac{1}{n+2}+\dots+\dfrac{1}{2n}

<1

Steven Zheng posted 4 days ago

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Answer

\because n < n+k <2n

\therefore \dfrac{1}{2n} <\dfrac{1}{n+k}<\dfrac{1}{n}

Steven Zheng posted 4 days ago