Nhận thấy $\frac{1}{2}\leq \frac{2}{3}$
$\frac{2}{3}\leq \frac{3}{4}$
...
$\frac{9999}{10000}\leq\frac{10000}{10001} $
$A^{2}\leq \frac{1}{2}\times \frac{2}{3}\times \frac{3}{4}\times ...\frac{9999}{10000}\times\frac{10000}{10001}=\frac{1}{10001} <\frac{1}{10000}$
$\Rightarrow A<0,01$(đpcm)