Question

[Nguyễn Nhật Anh]

Giúp mk vs !!!!!!!!!!!!!!!!!!!!! Please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

\(A=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{30}.CMR:\frac{5}{6}< A< \frac{77}{60}\)

Answer 1

[Bạch Dương]

Ta có :

  \(A=\left(\frac{1}{11}+\frac{1}{12}+...+\frac{1}{20}\right)+\left(\frac{1}{21}+\frac{1}{22}+...+\frac{1}{30}\right)\)

Ta thấy :

 \(\frac{1}{20}< \frac{1}{11}\)

 \(\frac{1}{20}< \frac{1}{12}\)

\(...\)

\(\frac{1}{20}< \frac{1}{19}\)

\(\Rightarrow\frac{1}{20}\cdot10< \frac{1}{11}+\frac{1}{12}+...+\frac{1}{20}\)

     \(\Rightarrow\frac{1}{2}< \frac{1}{11}+\frac{1}{12}+...+\frac{1}{20}\)⁽¹⁾

\(\frac{1}{30}< \frac{1}{21}\)

\(\frac{1}{30}< \frac{1}{22}\)

\(...\)

\(\frac{1}{30}< \frac{1}{29}\)

\(\Rightarrow\frac{1}{30}\cdot10< \frac{1}{21}+\frac{1}{22}+...+\frac{1}{30}\)

\(\Rightarrow\frac{1}{3}< \frac{1}{21}+\frac{1}{22}+...+\frac{1}{30}\)⁽²⁾

     Từ ^(1),(2) :

\(\Rightarrow\frac{1}{2}+\frac{1}{3}< \frac{1}{11}+\frac{1}{12}+...+\frac{1}{30}\)

\(\Rightarrow\frac{5}{6}< A\)

                                                          \(#Louis\)