Tính tổng biểu thức A = 1/2.5 + 1/5.8 + 1/8.11 + .. + 1/92.95 + 1/95.98
Giải thích
\[A = \frac{1}{{2 \cdot 5}} + \frac{1}{{5 \cdot 8}} + \frac{1}{{8 \cdot 11}} + ... + \frac{1}{{92 \cdot 95}} + \frac{1}{{95 \cdot 98}}\]
\[ = \frac{1}{3} \cdot \left( {\frac{3}{{2 \cdot 5}} + \frac{3}{{5 \cdot 8}} + \frac{3}{{8 \cdot 11}} + ... + \frac{3}{{92 \cdot 95}} + \frac{3}{{95 \cdot 98}}} \right)\]
\[ = \frac{1}{3}\left( {\frac{1}{2} - \frac{1}{5} + \frac{1}{5} - \frac{1}{8} + \frac{1}{8} - \frac{1}{{11}} + ... + \frac{1}{{92}} - \frac{1}{{95}} + \frac{1}{{95}} - \frac{1}{{98}}} \right)\]
\[ = \frac{1}{3}\left( {\frac{1}{2} - \frac{1}{{98}}} \right)\]
\[ = \frac{1}{3} \cdot \frac{{24}}{{49}} = \frac{8}{{49}}.\]