A = \(\left(\frac{1}{11}+\frac{1}{12}+.........+\frac{1}{20}\right)\) + \(\left(\frac{1}{21}+\frac{1}{22}+..........+\frac{1}{30}\right)\)+ \(\left(\frac{1}{31}+.....+\frac{1}{60}\right)\)+ ... + \(\frac{1}{70}\)
Nhận xét:
\(\frac{1}{11}\)+ \(\frac{1}{12}\)+ ........ + \(\frac{1}{20}\)> \(\frac{1}{20}\)+\(\frac{1}{20}\)+........+\(\frac{1}{20}\)> \(\frac{10}{20}\)>\(\frac{1}{2}\)
\(\frac{1}{21}+\frac{1}{22}+.......+\frac{1}{30}>\frac{30}{60}>\frac{1}{2}\)
\(\frac{1}{31}+......+\frac{1}{60}>\frac{1}{60}+\frac{1}{60}+.......+\frac{1}{60}>\frac{30}{60}>\frac{1}{2}\)
A > \(\frac{1}{2}+\frac{1}{3}+\frac{1}{2}+\frac{1}{61}+......+\frac{1}{70}>\frac{1}{2}+\frac{1}{3}+\frac{1}{2}>\frac{4}{3}\)