Cho \(S = \frac{1}{{1.2}} +...

D

- Hướng dẫn giải

Ta có: \(\frac{1}{{1.2}} = \frac{1}{1} - \frac{1}{2};\,\,\,\frac{1}{{2.3}} = \frac{1}{2} - \frac{1}{3};...\)

Nên \(\begin{array}{l}S = 1 - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + \frac{1}{3} - \frac{1}{4} + ... + \frac{1}{9} - \frac{1}{{10}}\\\,\,\,\,\, = 1 - \frac{1}{{10}} = \frac{9}{{10}}\end{array}\)