Ta có: A = \(\dfrac{1}{31}+\dfrac{1}{32}+\dfrac{1}{33}+...+\dfrac{1}{60}\)
A = \(\left(\dfrac{1}{31}+\dfrac{1}{32}+\dfrac{1}{33}+...+\dfrac{1}{45}\right)+\left(\dfrac{1}{46}+\dfrac{1}{47}+...+\dfrac{1}{60}\right)\)
Ta có: \(\dfrac{1}{31}>\dfrac{1}{45}\); \(\dfrac{1}{32}>\dfrac{1}{45}\); ...; \(\dfrac{1}{45}=\dfrac{1}{45}\)
\(\dfrac{1}{46}>\dfrac{1}{60}\); \(\dfrac{1}{47}>\dfrac{1}{60}\); ...; \(\dfrac{1}{60}=\dfrac{1}{60}\)
\(\Rightarrow\) A = \(\left(\dfrac{1}{31}+\dfrac{1}{32}+...+\dfrac{1}{45}\right)+\left(\dfrac{1}{46}+\dfrac{1}{47}+...+\dfrac{1}{60}\right)\) > \(15\cdot\dfrac{1}{45}+15\cdot\dfrac{1}{60}\)
A > \(\dfrac{1}{3}+\dfrac{1}{4}=\dfrac{7}{12}\) (đpcm)
Vậy A > \(\dfrac{7}{12}\)
Chúc bn học tốt!
A=1/31 1/32 1/33 ... 1/60. chứng minh A>7/12 - Hoc24
tham khảo nha
