a) Vì \(721< 834\Rightarrow\frac{5}{721}>\frac{5}{834}\)
b) Ta có \(\frac{4}{37}< \frac{5}{37}< \frac{5}{36}\Rightarrow\frac{4}{37}< \frac{5}{36}\)
c) Ta có \(\frac{1994}{1995}=1-\frac{1}{1995}\)
\(\frac{1999}{2000}=1-\frac{1}{2000}\)
Vì \(\frac{1}{1995}>\frac{1}{2000}\Rightarrow1-\frac{1}{1995}< 1-\frac{1}{2000}\Rightarrow\frac{1994}{1995}< \frac{1999}{2000}\)
d) Ta có :\(\frac{489}{487}=1+\frac{2}{487}\)
\(\frac{487}{485}=1+\frac{2}{485}\)
Vì \(\frac{2}{485}>\frac{2}{487}\Rightarrow1+\frac{2}{485}>1+\frac{2}{487}\Rightarrow\frac{489}{487}>\frac{487}{485}\)
e) Ta có : \(\frac{123.125+119}{124.125-177}=\frac{123.125+119}{\left(123+1\right).125-177}=\frac{123.125+119}{123.125+125-177}=\frac{123.125+119}{123.125-52}\)
\(=\frac{123.125-52+171}{123.125-52}=1+\frac{171}{123.125-52}>1\)
f) \(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{199.200}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{199}-\frac{1}{200}=1-\frac{1}{200}< 1\)
