Ta có: \(\frac{1}{101}+\frac{1}{102}+...+\frac{1}{209}+\frac{1}{300}>\frac{1}{300}.200\)
\(\Rightarrow\frac{1}{101}+\frac{1}{102}+...+\frac{1}{209}+\frac{1}{300}>\frac{2}{3}\)
Vậy \(\frac{1}{101}+\frac{1}{102}+...+\frac{1}{209}+\frac{1}{300}>\frac{2}{3}\left(đpcm\right)\)