Tính giá trị của biểu thức:\(A = \frac{1}{{2.5}} + \frac{1}{{5.8}} + \frac{1}{{8.11}} + ... + \frac{1}{{92.95}} + \frac{1}{{95.98}}.\)

* Hướng dẫn giải

\(\begin{array}{l}A = \frac{1}{{2.5}} + \frac{1}{{5.8}} + \frac{1}{{8.11}} + ... + \frac{1}{{92.95}} + \frac{1}{{95.98}}.\\A = \frac{1}{3}.\left( {\frac{3}{{2.5}} + \frac{3}{{5.8}} + \frac{3}{{8.11}} + ... + \frac{3}{{92.95}} + \frac{3}{{95.98}}} \right)\\A = \frac{1}{3}.\left( {\frac{1}{2} - \frac{1}{5} + \frac{1}{5} - \frac{1}{8} + \frac{1}{8} - \frac{1}{{11}} + ... + \frac{1}{{92}} - \frac{1}{{95}} + \frac{1}{{95}} - \frac{1}{{98}}} \right)\\A = \frac{1}{3}.\left( {\frac{1}{2} - \frac{1}{{98}}} \right)\\A = \frac{1}{3}.\frac{{48}}{{98}}\\A = \frac{{16}}{{98}}\end{array}\)

Vậy \(A = \frac{{16}}{{98}}\)

Chọn B