Ta có: \(A=\left(\frac14-1\right)\left(\frac19-1\right)\cdot\ldots\cdot\left(\frac{1}{400}-1\right)\)
\(=\left(\frac12-1\right)\left(\frac13-1\right)\cdot\ldots\cdot\left(\frac{1}{20}-1\right)\left(\frac12+1\right)\left(\frac13+1\right)\cdot\ldots\cdot\left(\frac{1}{20}+1\right)\)
\(=\frac{-1}{2}\cdot\frac{-2}{3}\cdot\ldots\cdot\frac{-19}{20}\cdot\frac32\cdot\frac43\cdot\ldots\cdot\frac{21}{20}\)
\(=-\frac{1}{20}\cdot\frac{21}{2}=-\frac{21}{40}\)
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