A=1/2.3/4.5/6.7/8.....4095/4096 và B=2/1.4/3.6/5.8/7....4096/4097. Chứng minh A<1/64
[tex]\dpi{100} A=\frac{1}{2}.\frac{3}{4}.\frac{5}{6}.....\frac{4095}{4096}<C=\frac{2}{3}.\frac{4}{5}.\frac{6}{7}.....\frac{4096}{4097}\\A<C\Rightarrow A.A<A.C=\frac{1}{2}.\frac{3}{4}.\frac{5}{6}.....\frac{4095}{4096}.\frac{2}{3}.\frac{4}{5}.\frac{6}{7}.....\frac{4096}{4097}=\frac{1}{4097}\\A.A<A.C=\frac{1}{4097}<\frac{1}{4096}=\frac{1}{64}.\frac{1}{64}\Rightarrow A<\frac{1}{64}[/tex]
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