Question

A=\(\frac{1}{15}+\frac{1}{16}+...+\frac{1}{44}\)

CMR: A >\(\frac{5}{6}\)

 

Answer 1

\(A=\left(\frac{1}{15}+\frac{1}{16}+\frac{1}{17}+...+\frac{1}{29}\right)+\left(\frac{1}{30}+\frac{1}{31}+\frac{1}{32}+...+\frac{1}{44}\right)\)

\(\frac{1}{15}>\frac{1}{30};\frac{1}{16}>\frac{1}{30};....;\frac{1}{29}>\frac{1}{30}\)

\(\frac{1}{30}>\frac{1}{45};\frac{1}{31}>\frac{1}{45};\frac{1}{32}>\frac{1}{45};...;\frac{1}{44}>\frac{1}{45}\)

Mà mỗi nhóm có 15 số hạng:

\(\Rightarrow A>\frac{15.1}{30}+\frac{15.1}{45}\)

\(A>\frac{5}{6}\)

Học tốt nhé bạn!

Answer 2

\(A=\left(\frac{1}{15}+\frac{1}{16}+\frac{1}{17}+...+\frac{1}{29}\right)+\left(\frac{1}{30}+\frac{1}{31}+\frac{1}{32}+...+\frac{1}{44}\right)\)

\(\frac{1}{15}>\frac{1}{30};\frac{1}{16}>\frac{1}{30};....;\frac{1}{29}>\frac{1}{30}\)

\(\frac{1}{30}>\frac{1}{45};\frac{1}{31}>\frac{1}{45};\frac{1}{32}>\frac{1}{45};...;\frac{1}{44}>\frac{1}{45}\)

Mà mỗi nhóm có 15 số hạng:

\(\Rightarrow A>\frac{15.1}{30}+\frac{15.1}{45}\)

\(A>\frac{5}{6}\)

Học tốt nhé bạn!

Answer 3

\(A=\left(\frac{1}{15}+\frac{1}{16}+\frac{1}{17}+...+\frac{1}{29}\right)+\left(\frac{1}{30}+\frac{1}{31}+\frac{1}{32}+...+\frac{1}{44}\right)\)

\(\frac{1}{15}>\frac{1}{30};\frac{1}{16}>\frac{1}{30};....;\frac{1}{29}>\frac{1}{30}\)

\(\frac{1}{30}>\frac{1}{45};\frac{1}{31}>\frac{1}{45};\frac{1}{32}>\frac{1}{45};...;\frac{1}{44}>\frac{1}{45}\)

Mà mỗi nhóm có 15 số hạng:

\(\Rightarrow A>\frac{15.1}{30}+\frac{15.1}{45}\)

\(A>\frac{5}{6}\)

Học tốt nhé bạn!