Tham khảo:

\(S=\dfrac{3}{10}+\dfrac{3}{11}+\dfrac{3}{12}+\dfrac{3}{13}+\dfrac{3}{14}\)

\(\Rightarrow S< \dfrac{3}{10}+\dfrac{3}{10}+\dfrac{3}{10}+\dfrac{3}{10}+\dfrac{3}{10}\)

\(\Rightarrow S< \dfrac{15}{10}< 2\)

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: \(\dfrac{3}{10}>\dfrac{3}{15}\)

\(\dfrac{3}{11}>\dfrac{3}{15}\)

\(\dfrac{3}{12}>\dfrac{3}{15}\)

\(\dfrac{3}{13}>\dfrac{3}{15}\)

\(\dfrac{3}{14}>\dfrac{3}{15}\)

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)

thank you

\(\frac{3}{10}+\frac{3}{11}+\frac{3}{12}+\frac{3}{13}+\frac{3}{14}\)

\(\Rightarrow\frac{3}{14}+\frac{3}{14}+\frac{3}{14}+\frac{3}{14}+\frac{3}{14}< S< \frac{3}{10}+\frac{3}{10}+\frac{3}{10}+\frac{3}{10}+\frac{3}{10}\)

\(\frac{3}{14}\times5< S< \frac{3}{10}\times5\Rightarrow\frac{15}{14}< S< \frac{3}{2}\)

mà \(\frac{15}{14}>1;\frac{3}{2}< 2\Rightarrow1< S< 2\)

giải\(s>\frac{3}{15}+\frac{3}{15}+\frac{3}{15}+\frac{3}{15}+\frac{3}{15}=\frac{15}{15}=1\)

\(s<\frac{3}{10}+\frac{3}{10}+\frac{3}{10}+\frac{3}{10}+\frac{3}{10}=\frac{15}{10}<\frac{20}{10}=2\)

vậy 1<s<2

=>s không thuộc N

Tự hỏi tự mình trả lời lun....?!?!?? :)

S=3.(\(\frac{1}{10}\)+\(\frac{1}{11}\)+\(\frac{1}{12}\)+\(\frac{1}{13}\)+\(\frac{1}{14}\))>3.(5.\(\frac{1}{14}\))>3.\(\frac{1}{3}\)=1

Vậy:S>1