Tính giá trị 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

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