x đâu rồi bạn

\(S=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}+\frac{1}{17}+\frac{1}{18}+\frac{1}{19}+\frac{1}{20}=0,6687714032\)

10 < 10 + 3

11 + 2=2 + 11

9 < 10 + 9

10 = 10 + 0

17 – 4 > 14 - 3

18 – 4 >12

15 > 15 – 1

17 + 1<17 + 2

12+ 5 > 16

16 =19 - 3

15 – 4 =10 + 1

19 – 3 >11

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

S>\(\frac{1}{2}\)

s>1/2

\(S=\frac{1}{11}+\frac{1}{12}+...+\frac{1}{20}\)

\(>\frac{1}{20}+\frac{1}{20}+...+\frac{1}{20}\)(10 số hạng) 

\(=10.\frac{1}{20}=\frac{1}{2}\).

Vậy \(S>\frac{1}{2}\).

Ta có:\(\frac{1}{11}>\frac{1}{20};\frac{1}{12}>\frac{1}{20};\frac{1}{13}>\frac{1}{20};....;\frac{1}{19}>\frac{1}{20}\)

\(\Rightarrow\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{20}>\frac{1}{20}+\frac{1}{20}+\frac{1}{20}+...+\frac{1}{20}\)(Có 10 phân số \(\frac{1}{20}\))

\(\Rightarrow\frac{1}{11}+\frac{1}{12}+...+\frac{1}{20}>\frac{10}{20}\)\(\Leftrightarrow S>\frac{10}{20}\)

Mà \(\frac{10}{20}=\frac{1}{2}\)nên

\(\Rightarrow S>\frac{1}{2}\)

ta thấy: 1/11;1/12;1/13;...;1/19;1/20 đều >1/20

=>1/11+1/12+...1/19+1/20>1/20+1/20...+1/20

1/11+1/12+...1/19+1/20>10/20

1/11+1/12+...1/19+1/20>1/2 vậy S>1/2

S > 1/2

 Chúc bn học tốt!

có  \(\frac{1}{20}\) bé nhất suy ra

"có 10 số hạng "\(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+......+\frac{1}{20}>\frac{1}{20}.10\)

\(VT>\frac{10}{20}=\frac{1}{2}\)

vì 1/11>1/20

     1/12>1/20...

     1/13>1/20

nên 1/11+1/12+,,,,+1/20>1/20+1/20+,,,,+1/20=10/20=1/2(rút gọn

                                    10 số 1/20

vậy S>1/2