Question

A=(1-1/4)×(1-1/9)×(1-1/16)×...×(1-1/400)

Answer 1

TA có: \(A=\left(1-\frac14\right)\left(1-\frac19\right)\cdot\ldots\cdot\left(1-\frac{1}{400}\right)\)

\(=\left(1-\frac12\right)\left(1-\frac13\right)\cdot\ldots\cdot\left(1-\frac{1}{20}\right)\left(1+\frac12\right)\cdot\left(1+\frac13\right)\cdot\ldots\cdot\left(1+\frac{1}{20}\right)\)

\(=\frac12\cdot\frac23\cdot\ldots\cdot\frac{19}{20}\cdot\frac32\cdot\frac43\cdot\ldots\cdot\frac{21}{2}=\frac{1}{20}\cdot\frac{21}{2}=\frac{21}{40}\)