Tính tích \(A = \frac{3}{4}.\frac{8}{9}.\frac{{15}}{{16}}...\frac{{899}}{{900}}\)
\(\begin{array}{l}
A = \frac{3}{4}.\frac{8}{9}.\frac{{15}}{{16}}...\frac{{899}}{{900}}\\
= \frac{{1.3}}{{2.2}}.\frac{{2.4}}{{3.3}}.\frac{{3.5}}{{4.4}}...\frac{{29.31}}{{30.30}}\\
= \frac{{1.2.3...29}}{{2.3.4...30}}.\frac{{3.4.5...31}}{{2.3.4...30}}\\
= \frac{1}{{30}}.\frac{{31}}{2} = \frac{{31}}{{60}}
\end{array}\)
-- Mod Toán 6
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