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3/10>3/15
3/11>3/15
3/12>3/15
3/13>3/15
3/14>3/15
=>S>3/15*5=15/15=1
3/11<3/10
3/12<3/10
3/13<3/10
3/14<3/10
=>3/11+3/12+3/13+3/14+3/10<3/10*5=15/10=3/2<2
=>1<S<2
\(\frac{3}{10}+\frac{3}{11}+\frac{3}{12}+\frac{3}{13}+\frac{3}{14}>\frac{3}{15}+\frac{3}{15}+\frac{3}{15}+\frac{3}{15}+\frac{3}{15}=\frac{15}{15}=1\)
\(\frac{3}{10}+\frac{3}{11}+\frac{3}{12}+\frac{3}{13}+\frac{3}{14}< \frac{3}{9}+\frac{3}{9}+\frac{3}{9}+\frac{3}{9}+\frac{3}{9}=\frac{15}{9}< \frac{18}{9}=2\)
Suy ra đpcm.
- 3/10 +3/11 +3/12 +3/13 +3/14 > 3/15 + 3/15 +3/15 +3/15 +3/15 = 15/15 =1
S < 3/10 +3/10 +3/10 + 3/10 + 3/10 = 15/ 10 < 20/10 =2
\(S=\dfrac{3}{10}+\dfrac{3}{11}+\dfrac{3}{12}+\dfrac{3}{13}+\dfrac{3}{14}\)
\(\Rightarrow S< \dfrac{3}{10}+\dfrac{3}{10}+\dfrac{3}{10}+\dfrac{3}{10}+\dfrac{3}{10}\)
\(\Rightarrow S< \dfrac{15}{10}< 2\)
Lại có \(S>\dfrac{3}{14}+\dfrac{3}{14}+\dfrac{3}{14}+\dfrac{3}{14}+\dfrac{3}{14}\)
\(\Rightarrow S>\dfrac{15}{14}>1\)
\(\Rightarrow1< S< 2\)
Ta có: S =3/10+3/11+3/12+3/13+3/14 = 3.(1/10+1/11+1/12+1/13+1/14) > 3.(1/15 + 1/15 + 1/15 + 1/15 + 1/15) = 3.5/15 = 1 => S > 1 (1)
S=3/10+3/11+3/12+3/13+3/14 = 3.(1/10+1/11+1/12+1/13+1/14) < 3.(1/10 + 1/10 + 1/10 + 1/10 + 1/10) = 3.5/10 = 3/2<2 =>S <2 (2)
Từ (1) va (2)
=> 1 < S < 2 (đpcm).
Chúc bạn học tập tốt :)
Ta có: \(\dfrac{3}{10}>\dfrac{3}{15}\)
\(\dfrac{3}{11}>\dfrac{3}{15}\)
\(\dfrac{3}{12}>\dfrac{3}{15}\)
\(\dfrac{3}{13}>\dfrac{3}{15}\)
\(\dfrac{3}{14}>\dfrac{3}{15}\)
Do đó: \(\dfrac{3}{10}+\dfrac{3}{11}+\dfrac{3}{12}+\dfrac{3}{13}+\dfrac{3}{14}>\dfrac{3}{15}+\dfrac{3}{15}+\dfrac{3}{15}+\dfrac{3}{15}+\dfrac{3}{15}=1\)
hay 1<S(1)
Ta có: \(\dfrac{3}{11}< \dfrac{3}{10}\)
\(\dfrac{3}{12}< \dfrac{3}{10}\)
\(\dfrac{3}{13}< \dfrac{3}{10}\)
\(\dfrac{3}{14}< \dfrac{3}{10}\)
Do đó: \(\dfrac{3}{11}+\dfrac{3}{12}+\dfrac{3}{13}+\dfrac{3}{14}< \dfrac{3}{10}+\dfrac{3}{10}+\dfrac{3}{10}+\dfrac{3}{10}=\dfrac{12}{10}\)
\(\Leftrightarrow S< \dfrac{15}{10}=\dfrac{3}{2}< 2\)(2)
Từ (1) và (2) suy ra 1<S<2(đpcm)
\(S=\dfrac{3}{10}+\dfrac{3}{11}+\dfrac{3}{12}+\dfrac{3}{13}+\dfrac{3}{14}\)
Ta thấy:
\(\dfrac{3}{10}>\dfrac{3}{15}\\\dfrac{3}{11}>\dfrac{3}{15}\\ \dfrac{3}{12}>\dfrac{3}{15}\\ \dfrac{3}{13}>\dfrac{3}{15}\\ \dfrac{3}{14}>\dfrac{3}{15} \)
\(\Rightarrow S=\dfrac{3}{10}+\dfrac{3}{11}+\dfrac{3}{12}+\dfrac{3}{13}+\dfrac{3}{14}>5\cdot\dfrac{3}{15}\\ S=\dfrac{3}{10}+\dfrac{3}{11}+\dfrac{3}{12}+\dfrac{3}{13}+\dfrac{3}{14}>1\left(1\right)\)
Mặt khác:
\(\dfrac{3}{10}< \dfrac{3}{9}\\ \dfrac{3}{11}< \dfrac{3}{9}\\ \dfrac{3}{12}< \dfrac{3}{9}\\ \dfrac{3}{13}< \dfrac{3}{9}\\ \dfrac{3}{14}>\dfrac{3}{9}\)
\(\Rightarrow S=\dfrac{3}{10}+\dfrac{3}{11}+\dfrac{3}{12}+\dfrac{3}{13}+\dfrac{3}{14}< 5\cdot\dfrac{3}{9}\\ S=\dfrac{3}{10}+\dfrac{3}{11}+\dfrac{3}{12}+\dfrac{3}{13}+\dfrac{3}{14}< \dfrac{5}{3}< 2\left(2\right)\)
Từ (1) và (2) ta có: \(1< S< 2\)
Ta có: \(\frac{3}{10}>\frac{3}{15}\)
\(\frac{3}{11}>\frac{3}{15}\)
\(\frac{3}{12}>\frac{3}{15}\)
\(\frac{3}{13}>\frac{3}{15}\)
\(\frac{3}{14}>\frac{3}{15}\)
Cộng với vế ta được: \(\frac{3}{10}+\frac{3}{11}+\frac{3}{12}+\frac{3}{13}+\frac{3}{14}>\frac{3}{15}+\frac{3}{15}+\frac{3}{15}+\frac{3}{15}+\frac{3}{15}=\frac{15}{15}=1\)(1)
Tương tự ta có: \(\frac{3}{10}=\frac{3}{10}\)
\(\frac{3}{11}< \frac{3}{10}\)
\(\frac{3}{12}< \frac{3}{10}\)
\(\frac{3}{13}< \frac{3}{10}\)
\(\frac{3}{14}< \frac{3}{10}\)
Cộng với vế ta được: \(\frac{3}{10}+\frac{3}{11}+\frac{3}{12}+\frac{3}{13}+\frac{3}{14}< \frac{3}{10}+\frac{3}{10}+\frac{3}{10}+\frac{3}{10}+\frac{3}{10}=\frac{15}{10}\)
Mà \(\frac{15}{10}< \frac{20}{10}=2\)(2)
Từ (1) và (2) => đpcm