Chứng minh rằng: B = 1/6 + 1/7 + ... + 1/18 + 1/19 < 2

* Hướng dẫn giải

$$\begin{gathered} \text{B}=\frac{1}{6}+\frac{1}{7}+\mathrm{...}+\frac{1}{18}+\frac{1}{19} \\ =\left(\frac{1}{6}+\mathrm{...}+\frac{1}{9}\right)+\left(\frac{1}{10}+\mathrm{...}+\frac{1}{19}\right)<\underset{4s}{\underbrace{\frac{1}{4}+\mathrm{...}+\frac{1}{4}}}+\underset{10s}{\underbrace{\frac{1}{10}+\mathrm{...}+\frac{1}{10}}}=1+1=2 \end{gathered}$$