Question

Tính nhanh:

\(1\frac{1}{3}x2\frac{1}{4}x3\frac{1}{5}x4\frac{1}{6}x5\frac{1}{7}x6\frac{1}{8}x7\frac{1}{9}x8\frac{1}{10}\)

Answer 1

\(1\frac{1}{3}\times2\frac{1}{4}\times...\times8\frac{1}{10}\)

\(=\frac{4}{3}\times\frac{9}{4}\times...\times\frac{81}{10}\)

\(=\frac{4\times9\times...\times81}{3\times4\times...\times10}\)

\(=\frac{2\times2\times3\times3\times...\times9\times9}{3\times4\times5\times...\times10}\)

\(=\frac{\left(2\times3\times4\times...\times9\right)\times\left(2\times3\times4\times...\times9\right)}{3\times4\times5\times...\times10}\)

\(=\frac{2\times2\times3\times...\times9}{10}\)

\(=2\times3\times4\times6\times...\times9\)

\(=72576\)