Chứng minh rằng: A= 1/1.2 +1/1.3 +1/1.4 +...+ 1/2.2 > 1/2

* Hướng dẫn giải

a) $A=\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\mathrm{...}+\frac{1}{22}>\underset{11\text{s}}{\underbrace{\frac{1}{22}+\frac{1}{22}+\mathrm{...}\frac{1}{22}}}=\frac{11}{22}=\frac{1}{2}.$

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

c) $C=\frac{1}{10}+\left(\frac{1}{11}+\mathrm{...}+\frac{1}{100}\right)>\frac{1}{10}+\underset{90so}{\underbrace{\left(\frac{1}{100}=\mathrm{...}+\frac{1}{100}\right)}}=\frac{1}{10}+\frac{90}{100}=1$