Ta có: \(\frac{1}{5}< \frac{1}{2}=\frac{1}{1.2}\)
\(\frac{1}{7}< \frac{1}{6}=\frac{1}{2.3}\)
.......
\(\frac{1}{101}< \frac{1}{90}=\frac{1}{9.10}\)
=>0<A<\(\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{9.10}\)
<=>0<A<\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-....+\frac{1}{9}-\frac{1}{10}\)=1-\(\frac{1}{10}\)
Có 1 -\(\frac{1}{10}\)<1
=>0<A<1
=> A ko là số tự nhiên