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:1/11>1/20;1/12>1/20;........;1/20=1/20
=>1/11+1/12+1/13+...+1/20>10/20=1/2
Vay 1/11+1/12+...+1/20>1/2
Em có thể tham khảo video:
https://www.youtube.com/watch?v=T60Nn28G6rg&list=PLq0mRSDfY0BAMTu98fNHi-Lg_E9BWDYhV&index=8