Chứng minh A < 1.

Lời giải:

A < \(\frac{1}{{1.2}} + \frac{1}{{2.3}} + \frac{1}{{3.4}} + ... + \frac{1}{{99.100}}\)

\[A < 1 - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + ... + \frac{1}{{99}} - \frac{1}{{100}} = 1 - \frac{1}{{100}} < 1\]