Ta có : \(\displaystyle{1 \over {11}} > {1 \over {20}};{1 \over {12}} > {1 \over {20}};....;{1 \over {19}} > {1 \over {20}};\)
\( \Rightarrow\displaystyle{\rm{S}} > {1 \over {20}} + {1 \over {20}} + {1 \over {20}} + {1 \over {20}} + {1 \over {20}} \)\(\displaystyle+ {1 \over {20}} + {1 \over {20}} + {1 \over {20}} + {1 \over {20}} + {1 \over {20}} \)
\(\displaystyle \Rightarrow S> {{10} \over {20}} =\dfrac{1}{2}\)
Vậy \(\displaystyle{\rm{S}} > {1 \over 2}.\)
