so sánh S và 1/2 bieetsS=1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(S=\frac{1}{11}+\frac{1}{12}+...+\frac{1}{20}\)
\(>\frac{1}{20}+\frac{1}{20}+...+\frac{1}{20}\)(10 số hạng)
\(=10.\frac{1}{20}=\frac{1}{2}\).
Vậy \(S>\frac{1}{2}\).
![](https://rs.olm.vn/images/avt/0.png?1311)
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
![](https://rs.olm.vn/images/avt/0.png?1311)
Ai trả lời mik sẽ k cho người đó bất kể số lượng người
![](https://rs.olm.vn/images/avt/0.png?1311)
có \(\frac{1}{20}\) bé nhất suy ra
"có 10 số hạng "\(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+......+\frac{1}{20}>\frac{1}{20}.10\)
\(VT>\frac{10}{20}=\frac{1}{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
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
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{11}\)> \(\frac{1}{20}\)
\(\frac{1}{12}\)> \(\frac{1}{20}\)
.
.
.
\(\frac{1}{19}\)>\(\frac{1}{20}\)
\(\frac{1}{20}\)= \(\frac{1}{20}\)
=> S = 1/11+1/12+...+1/20>1/20+1/20+1/20+1/20+1/20+1/20+1/20+1/20+1/20+1/20=10*1/20=1/2 (đpcm)
Ta có:
\(\frac{1}{11}>\frac{1}{20}\)
\(\frac{1}{12}>\frac{1}{20}\)
.............
\(\frac{1}{20}=\frac{1}{20}\)
\(\Rightarrow\frac{1}{11}+\frac{1}{12}+...+\frac{1}{20}>\frac{1}{20}+\frac{1}{20}+...+\frac{1}{20}\) ( 10 phân số \(\frac{1}{20}\))
\(\Leftrightarrow\frac{10.1}{20}=\frac{10}{20}=\frac{1}{2}\)
Vì \(\frac{1}{20}+\frac{1}{20}+...+\frac{1}{20}=\frac{1}{2}\). Mà \(\frac{1}{11}+\frac{1}{12}+...+\frac{1}{20}>\frac{1}{20}\Rightarrow\frac{1}{11}+\frac{1}{12}+...+\frac{1}{20}>\frac{1}{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Số lượng số của S là :
\(\left(20-11\right):1+1=10\)( số )
Ta có :
\(\frac{1}{11}>\frac{1}{20};\frac{1}{12}>\frac{1}{20};...;\frac{1}{19}>\frac{1}{20};\frac{1}{20}=\frac{1}{20}\)
\(\Rightarrow\frac{1}{11}+\frac{1}{12}+...+\frac{1}{20}>\frac{1}{20}+\frac{1}{20}+...+\frac{1}{20}\)
\(\Rightarrow S>\frac{1}{20}.10\)
\(\Rightarrow S>\frac{1}{2}\)
Vậy \(S>\frac{1}{2}\)
Ta có:
1/11 + 1/12 + 1/13 + ....................... + 1/ 20 > 1/20 +1/20 +1/ 20 +1/20 +1/20 +1/20 +1/20 +1/ 20 +1/20 +1/20 = 1/2
=> S > 1/2
Vậy S > 1/2
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(S=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}+\frac{1}{17}+\frac{1}{18}+\frac{1}{19}+\frac{1}{20}>\frac{1}{20}+...+\frac{1}{20}\)(10 số \(\frac{1}{20}\))
=\(\frac{1}{20}.10=\frac{1}{2}\)
vậy S>1/2
Ta có: \(\dfrac{1}{11}>\dfrac{1}{20};\dfrac{1}{12}>\dfrac{1}{20};\dfrac{1}{13}>\dfrac{1}{20};...;\dfrac{1}{19}>\dfrac{1}{20}\)
\(\Rightarrow\dfrac{1}{11}+\dfrac{1}{12}+\dfrac{1}{13}+...+\dfrac{1}{19}+\dfrac{1}{20}>\dfrac{1}{20}+\dfrac{1}{20}+\dfrac{1}{20}+...+\dfrac{1}{20}+\dfrac{1}{20}\)
\(\Rightarrow\dfrac{1}{11}+\dfrac{1}{12}+\dfrac{1}{13}+...+\dfrac{1}{19}+\dfrac{1}{20}>\dfrac{10}{20}\)
=> \(S>\dfrac{1}{2}\)
\(\dfrac{1}{11}>\dfrac{1}{20};\dfrac{1}{12}>\dfrac{1}{20};\dfrac{1}{13}>\dfrac{1}{20};...;\dfrac{1}{19}>\dfrac{1}{20}\\ =>S>\dfrac{1}{20}+\dfrac{1}{20}+\dfrac{1}{20}+...+\dfrac{1}{20}+\dfrac{1}{20}\\ =>S>\dfrac{1}{20}\times10\\ =>S>\dfrac{1}{2}\)