Tính nhanh tổng \(S,\) với \(S = \frac{2}{{3.5}} + \frac{2}{{5.7}} + \frac{2}{{7.9}} + ... + \frac{2}{{2017.2019}}\).

* Hướng dẫn giải

Ta có:

\(\begin{array}{l}S = \frac{2}{{3.5}} + \frac{2}{{5.7}} + \frac{2}{{7.9}} + ... + \frac{2}{{2017.2019}}\\\,\,\,\, = \frac{1}{3} - \frac{1}{5} + \frac{1}{5} - \frac{1}{7} + \frac{1}{7} - \frac{1}{9} + ... + \frac{1}{{2017}} - \frac{1}{{2019}}\\\,\,\,\, = \frac{1}{3} - \frac{1}{{2019}}\\\,\,\,\, = \frac{{672}}{{2019}} = \frac{{224}}{{673}}\end{array}\)

Vậy \(S = \frac{{224}}{{673}}\)

Chọn B