Tham khảo:
Ta có các phân số 1/11 ; 1/12 ; 1/13 ; 1/14 ; 1/15 ; 1/16 ; 1/17 ; 1/18 ; 1/19 đều lớn hơn 1/20
Do đó : 1/11 + 1/12 + 1/13 + 1/14 + 1/15 + 1/16 + 1/17 + 1/18 + 1/19 + 1/20 > 1/20 + 1/20 + ;...+ 1/20 ( có 10 phân số 1/20 )
1/11 + 1/12 + 1/13 + 1/14 + 1/15 + 1 /16 + 1/17 + 1/18 + 1/19 + 1/20 > 10/20
1/11 + 1/12 + 1/13 + 1/14 + 1/15 + 1 /16 + 1/17 + 1/18 + 1/19 + 1/20 > 1/2
Vậy : S > 1/2
Ta có: \(\dfrac{1}{2}=\dfrac{10}{20}=\dfrac{1}{20}+\dfrac{1}{20}+...+\dfrac{1}{20}\) ( Có 10 số \(\dfrac{1}{20}\) )
Mà \(\dfrac{1}{20}< \dfrac{1}{19}:\dfrac{1}{20}< \dfrac{1}{18}:...:\dfrac{1}{20}< \dfrac{1}{11}\)
\(\Rightarrow\dfrac{1}{20}+\dfrac{1}{20}+...+\dfrac{1}{20}< \dfrac{1}{20}+\dfrac{1}{19}+\dfrac{1}{18}+...+\dfrac{1}{11}\)
\(\Rightarrow A=B\)
