+ Ta có 3/10>3/15; 3/11>3/15; 3/12>3/15; 3/13>3/15; 3/14>3/15
=> S> 3/15+3/15+3/15+3/15+3/15=15/15=1
+ Ta có 3/10<3/8; 3/11<3/8; 3/12<3/8; 3/13<3/8; 3/14<3/8
=> S<3/8+3/8+3/8+3/8+3/8=15/8<2
=> 1<S<2
\(S=\frac{3}{10}+\frac{3}{11}+\frac{3}{12}+\frac{3}{13}+\frac{3}{14}>\frac{3}{15}+\frac{3}{15}+\frac{3}{15}+\frac{3}{15}+\frac{3}{15}\)
mà \(\frac{3}{15}+\frac{3}{15}+\frac{3}{15}+\frac{3}{15}+\frac{3}{15}=\frac{15}{15}=1\)
\(\Rightarrow\frac{3}{10}+\frac{3}{11}+\frac{3}{13}+\frac{3}{14}>1\) (1)
Ta có: \(S=\frac{3}{10}+\frac{3}{11}+\frac{3}{12}+\frac{3}{13}+\frac{3}{14}< \frac{3}{10}+\frac{3}{10}+\frac{3}{10}+\frac{3}{10}+\frac{3}{10}\)mà \(\frac{3}{10}+\frac{3}{10}+\frac{3}{10}+\frac{3}{10}+\frac{3}{10}=\frac{15}{10}< \frac{20}{10}=2\)
\(\Rightarrow\frac{3}{10}+\frac{3}{11}+\frac{3}{12}+\frac{3}{13}+\frac{3}{14}< 2\) (1)
Từ (1) và (2) => 1<S<2
\(S=\frac{3}{10}+\frac{3}{11}+\frac{3}{12}+\frac{3}{13}+\frac{3}{14}>\frac{3}{15}+\frac{3}{15}+\frac{3}{15}+\frac{3}{15}+\frac{3}{15}\)
mà \(\frac{3}{15}+\frac{3}{15}+\frac{3}{15}+\frac{3}{15}+\frac{3}{15}=\frac{15}{15}=1\)
=>S>1 (1)
Ta có: \(S=\frac{3}{10}+\frac{3}{11}+\frac{3}{12}+\frac{3}{13}+\frac{3}{14}< \frac{3}{10}+\frac{3}{10}+\frac{3}{10}+\frac{3}{10}+\frac{3}{10}\)mà \(\frac{3}{10}+\frac{3}{10}+\frac{3}{10}+\frac{3}{10}+\frac{3}{10}=\frac{15}{10}< \frac{20}{10}=2\)
=> S<2 (2)
Từ (1) và (2) => 1<S<2
Có \(\frac{2}{10}< \frac{3}{10}\)
\(\frac{2}{10}< \frac{3}{11}\)
...
\(\frac{2}{10}< \frac{3}{14}\)
=> \(\frac{2}{10}+\frac{2}{10}+\frac{2}{10}+\frac{2}{10}+\frac{2}{10}< \frac{3}{10}+\frac{3}{11}+\frac{3}{12}+\frac{3}{13}+\frac{3}{14}\)
=> \(5.\frac{2}{10}< S\)
=> \(1< S\)(1)
Có: \(\frac{3}{10}< \frac{4}{10}\)
\(\frac{3}{11}< \frac{4}{10}\)
...
\(\frac{3}{14}< \frac{4}{10}\)
=> \(\frac{3}{10}+\frac{3}{11}+\frac{3}{12}+\frac{3}{13}+\frac{3}{14}< \frac{4}{10}+\frac{4}{10}+\frac{4}{10}+\frac{4}{10}+\frac{4}{10}\)
=>\(S< 5.\frac{4}{10}\)
=>\(S< 2\)(2)
Từ (1) và (2)
=> 1<S<2