Question

[Lý Huyền Trang]

CMR:

B=1/12+1/13+...+1/22 < 1/2

D=1/5+1/6+....+1/17 < 2

HELP ME !!!!!

Answer 1

[Nhật Hạ]

Hình như sai đề :) T sửa lại nhé

\(B=\frac{1}{12}+\frac{1}{13}+...+\frac{1}{22}>\frac{1}{2}\)

B có 11 số hạng

Ta có: \(\frac{1}{12}>\frac{1}{22}\)

           \(\frac{1}{13}>\frac{1}{22}\)

               ............

             \(\frac{1}{22}=\frac{1}{22}\)

\(\Rightarrow B>\left(\frac{1}{22}+\frac{1}{22}+...+\frac{1}{22}\right)=\frac{11}{22}=\frac{1}{2}\)

Answer 2

[Nhật Hạ]

\(D=\frac{1}{5}+\frac{1}{6}+...+\frac{1}{17}< 2\)

Ta có: \(\frac{1}{5}=\frac{1}{5};\frac{1}{6}< \frac{1}{5};...;\frac{1}{10}< \frac{1}{5}\)

\(\Rightarrow\frac{1}{5}+\frac{1}{6}+...+\frac{1}{10}< (\frac{1}{5}+\frac{1}{5}+...+\frac{1}{5})=\frac{6}{5}\)(1)

Lại có: \(\frac{1}{11}=\frac{1}{11};\frac{1}{12}< \frac{1}{11};\frac{1}{13}< \frac{1}{11};...;\frac{1}{17}< \frac{1}{11}\)

\(\Rightarrow\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{17}< (\frac{1}{11}+\frac{1}{11}+\frac{1}{11}+...+\frac{1}{11})=\frac{7}{11}\)(2)

Từ (1), (2) \(\Rightarrow D< \frac{6}{5}+\frac{7}{11}=\frac{101}{55}< \frac{110}{55}=2\) 

P/s: Hoq chắc :<