Tính giá trị của biểu thức \(C = \frac{3}{{1.3}} + \frac{3}{{3.5}} + \frac{3}{{5.7}} + ... + \frac{3}{{95.97}} + \frac{3}{{97.99}}\).
Giải thích
Ta có: \(C = \frac{3}{{1.3}} + \frac{3}{{3.5}} + \frac{3}{{5.7}} + ... + \frac{3}{{95.97}} + \frac{3}{{97.99}}\)
\(C = 3\left( {\frac{1}{{1.3}} + \frac{1}{{3.5}} + \frac{1}{{5.7}} + ... + \frac{1}{{95.97}} + \frac{1}{{97.99}}} \right)\)
\(C = \frac{3}{2}\left( {\frac{2}{{1.3}} + \frac{2}{{3.5}} + \frac{2}{{5.7}} + ... + \frac{2}{{95.97}} + \frac{2}{{97.99}}} \right)\)
\(C = \frac{3}{2}\left( {1 - \frac{1}{3} + \frac{1}{3} - \frac{1}{5} + \frac{1}{5} - \frac{1}{7} + ... + \frac{1}{{95}} - \frac{1}{{97}} + \frac{1}{{97}} - \frac{1}{{99}}} \right)\)
\(C = \frac{3}{2}\left( {1 - \frac{1}{{99}}} \right)\)
\(C = \frac{3}{2}.\frac{{98}}{{99}}\)
\(C = \frac{{49}}{{33}}.\)
Vậy \(C = \frac{{49}}{{33}}.\)