Question

Chứng minh:

C = \(\dfrac{1}{5}+\dfrac{1}{6}+\dfrac{1}{7}+...+\dfrac{1}{17}< 2\)

Answer 1

1/5<2;1/6<2;...;1/17<2

suy ra 1/5+1/6+1/7+...+1/17<2

Answer 2

\(\dfrac{1}{5}+\dfrac{1}{6}+\dfrac{1}{7}+...+\dfrac{1}{17}\)

\(=\left(\dfrac{1}{5}+\dfrac{1}{6}+...+\dfrac{1}{10}\right)+\left(\dfrac{1}{11}+...+\dfrac{1}{17}\right)< \dfrac{1}{5}.6+\dfrac{1}{11}.7=\dfrac{6}{5}+\dfrac{7}{11}\)

\(=1\dfrac{46}{55}< 2\)

\(\Rightarrow dpcm\)