tính nhanh:
(1- 1/2)x(1-1/3)x(1-1/4)x(1-1/5)
(1- 3/4)x(1-3/7)x(1-3/10)x(1-1/13)x...x(1- 3/97)x(1- 3/100)
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\(\left(1-\dfrac{1}{2}\right)\times\left(1-\dfrac{1}{3}\right)\times\left(1-\dfrac{1}{4}\right)\times\left(1-\dfrac{1}{5}\right)\\ =\dfrac{1}{2}\times\dfrac{2}{3}\times\dfrac{3}{4}\times\dfrac{4}{5}\\ =\dfrac{1}{5}\\ ===============\\ \left(1-\dfrac{3}{4}\right)\times\left(1-\dfrac{3}{7}\right)\times\left(1-\dfrac{3}{10}\right)\times...\times\left(1-\dfrac{3}{97}\right)\times\left(1-\dfrac{3}{100}\right)\\ =\dfrac{1}{4}\times\dfrac{4}{7}\times\dfrac{7}{10}\times...\times\dfrac{94}{97}\times\dfrac{97}{100}\\ =\dfrac{1}{100}\)
\(\left(1-\dfrac{1}{2}\right)\times\left(1-\dfrac{1}{3}\right)\times\left(1-\dfrac{1}{4}\right)\times\left(1-\dfrac{1}{5}\right)\)
\(=\dfrac{1}{2}\times\dfrac{2}{3}\times\dfrac{3}{4}\times\dfrac{4}{5}\)
\(=\dfrac{1\times2\times3\times4}{2\times3\times4\times5}\)
\(=\dfrac{1}{5}\)
\(\left(1-\dfrac{3}{4}\right)\times\left(1-\dfrac{3}{7}\right)\times\left(1-\dfrac{3}{10}\right)\times\left(1-\dfrac{3}{13}\right)\times...\times\left(1-\dfrac{3}{97}\right)\times\left(1-\dfrac{3}{100}\right)\)
\(=\dfrac{1}{4}\times\dfrac{4}{7}\times\dfrac{7}{10}\times\dfrac{10}{13}\times...\times\dfrac{94}{97}\times\dfrac{97}{100}\)
\(=\dfrac{1\times4\times7\times10\times...\times94\times97}{4\times7\times10\times13\times...\times97\times100}\)
\(=\dfrac{1}{100}\)