Question

Chứng tỏ

A = \(\dfrac{1}{12}+\dfrac{1}{13}+\dfrac{1}{14}+...+\dfrac{1}{22}>\dfrac{1}{2}\)

Answer 1

\(\dfrac{1}{12}>\dfrac{1}{22};\dfrac{1}{13}>\dfrac{1}{22};...;\dfrac{1}{21}>\dfrac{1}{22};\dfrac{1}{22}=\dfrac{1}{22}\)

\(\Rightarrow\dfrac{1}{12}+\dfrac{1}{13}+\dfrac{1}{14}+...+\dfrac{1}{22}>\dfrac{1}{22}.11\) (do A có 11 số hạng)

\(\Leftrightarrow A>\dfrac{11}{22}=\dfrac{1}{2}\) ( đpcm)