+)Ta có:\(A=\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+..........+\frac{1}{99}+\frac{1}{100}\)(có (100-10):1+1=91 số hạng)
\(\Rightarrow A=\left(\frac{1}{10}+\frac{1}{11}+.........+\frac{1}{54}\right)+\frac{1}{55}+\left(\frac{1}{56}+\frac{1}{57}+.............+\frac{1}{100}\right)>\)
\(\left(\frac{1}{54}+\frac{1}{54}+........+\frac{1}{54}\right)+\frac{1}{55}+\left(\frac{1}{100}+\frac{1}{100}+........+\frac{1}{100}\right)\)
\(\Rightarrow A>\frac{45}{54}+\frac{1}{55}+\frac{45}{100}=\frac{5}{6}+\frac{1}{55}+\frac{9}{20}=\frac{5}{6}+\frac{9}{20}+\frac{1}{55}=\frac{50}{60}+\frac{27}{60}+\frac{1}{55}\)\(=\frac{77}{60}+\frac{1}{55}>1\)(vì \(\frac{77}{60}>1\))
\(\Rightarrow A>1\)(ĐPCM)
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