Question

Tính nhanh: Hãy chứng tỏ rằng 1/6+1/7+1/8+1/9+1/10>1/2

Answer 1

Ta có : \(\dfrac{1}{6}>\dfrac{1}{10}\)

\(\dfrac{1}{7}>\dfrac{1}{10}\)

\(\dfrac{1}{8}>\dfrac{1}{10}\)

\(\dfrac{1}{9}>\dfrac{1}{10}\)

\(\dfrac{1}{10}=\dfrac{1}{10}\)

Cộng tất cả các vế ( phải theo phải ) ( trái theo trái ta được )

\(\dfrac{1}{6}+\dfrac{1}{7}+\dfrac{1}{8}+\dfrac{1}{9}+\dfrac{1}{10}>\dfrac{1}{10}+\dfrac{1}{10}+\dfrac{1}{10}+\dfrac{1}{10}+\dfrac{1}{10}\)

\(\Rightarrow\dfrac{1}{6}+\dfrac{1}{7}+\dfrac{1}{8}+\dfrac{1}{9}+\dfrac{1}{10}>\dfrac{5}{10}=\dfrac{1}{2}\)

Answer 2

Ta có:
\(\dfrac{1}{6}>\dfrac{1}{10}\)
\(\dfrac{1}{7}>\dfrac{1}{10}\)
\(\dfrac{1}{8}>\dfrac{1}{10}\)
\(\dfrac{1}{9}>\dfrac{1}{10}\)
\(\dfrac{1}{10}=\dfrac{1}{10}\)
Do đó ta có:
\(\dfrac{1}{6}+\dfrac{1}{7}+\dfrac{1}{8}+\dfrac{1}{9}+\dfrac{1}{10}>\dfrac{1}{10}+\dfrac{1}{10}+\dfrac{1}{10}+\dfrac{1}{10}+\dfrac{1}{10}\)
\(\Rightarrow\dfrac{1}{6}+\dfrac{1}{7}+\dfrac{1}{8}+\dfrac{1}{9}+\dfrac{1}{10}>\dfrac{1}{10}\times5\)
\(\Rightarrow\dfrac{1}{6}+\dfrac{1}{7}+\dfrac{1}{8}+\dfrac{1}{9}+\dfrac{1}{10}>\dfrac{5}{10}=\dfrac{1}{2}\)
Vậy \(\dfrac{1}{6}+\dfrac{1}{7}+\dfrac{1}{8}+\dfrac{1}{9}+\dfrac{1}{10}>\dfrac{1}{2}\)