Question

TÍNH \(\left(1-\frac{1}{99}\right)\times\left(1-\frac{1}{100}\right)\times......\times\left(1-\frac{1}{2006}\right)\)

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Answer 1

\(\left(1-\frac{1}{99}\right).\left(1-\frac{1}{100}\right).....\left(1-\frac{1}{2006}\right)\)

\(=\left(\frac{99}{99}-\frac{1}{99}\right).\left(\frac{100}{100}-\frac{1}{100}\right).....\left(\frac{2006}{2006}-\frac{1}{2006}\right)\)

\(=\frac{98}{99}.\frac{99}{100}......\frac{2005}{2006}\)

\(=\frac{98.99.....2005}{99.100....2006}\)

\(=\frac{98}{2006}=\frac{49}{2006}\)

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