Chứng minh rằng: A= 1/11+1/12+1/13+...=1/20>1/2

* Hướng dẫn giải

a) $A>\underset{10\text{s}o}{\underbrace{\frac{1}{20}+\frac{1}{20}+\mathrm{...}+\frac{1}{20}}}=\frac{10}{20}=\frac{1}{2}.$

b) $B=\left(\frac{1}{5}+\mathrm{...}\frac{1}{9}\right)+\left(\frac{1}{10}+\mathrm{...}+\frac{1}{17}\right)<\underset{\text{5s}o}{\underbrace{\frac{1}{5}+\mathrm{...}+\frac{1}{5}}}+\underset{\text{8s}o}{\underbrace{\frac{1}{8}+\mathrm{...}+\frac{1}{8}}}=2$

c) $C=\frac{1}{10}+\left(\frac{1}{11}+\frac{1}{12}\mathrm{...}+\frac{1}{18}+\frac{1}{19}\right)<\frac{1}{10}+\underset{9\text{s}o}{\underbrace{\frac{1}{10}+\mathrm{...}\frac{1}{10}}}=1$