Tính \(D = \frac{{{2^2}}}{3} \cdot \frac{{{3^2}}}{8} \cdot \frac{{{4^2}}}{{15}} \cdot \frac{{{5^2}}}{{24}} \cdot \frac{{{6^2}}}{{35}} \cdot \frac{{{7^2}}}{{48}} \cdot \frac{{{8^2}}}{{63}} \cdot \frac{{{9^2}}}{{80}}\)
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Lời giải:
Báo saiTa có
\(\begin{array}{l} D = \frac{{{2^2}}}{3} \cdot \frac{{{3^2}}}{8} \cdot \frac{{{4^2}}}{{15}} \cdot \frac{{{5^2}}}{{24}} \cdot \frac{{{6^2}}}{{35}} \cdot \frac{{{7^2}}}{{48}} \cdot \frac{{{8^2}}}{{63}} \cdot \frac{{{9^2}}}{{80}}\\ D = \frac{{2.2}}{{1.3}} \cdot \frac{{3.3}}{{2.4}} \cdot \frac{{4.4}}{{3.5}} \ldots \frac{{8.8}}{{7.9}} \cdot \frac{{9.9}}{{8.10}} = \frac{{(2.3.4 \ldots 8.9)(2.3.4 \ldots 8.9)}}{{(1.2.3 \ldots 7.8)(3.4.5 \ldots 9.10)}} = \frac{{9.2}}{{10}} = \frac{9}{5} \end{array}\)
