Question

[Châu Trần Như Ý]

1. Tính nhanh: 

A = ( 1 -\(\frac{1}{3}\)).( 1 -\(\frac{1}{5}\)).( 1 -\(\frac{1}{7}\)).( 1 -\(\frac{1}{9}\)).( 1 -\(\frac{1}{11}\)).( 1 - \(\frac{1}{2}\)).( 1 -\(\frac{1}{4}\)).( 1 -\(\frac{1}{6}\)).( 1 -\(\frac{1}{8}\)).( 1 -\(\frac{1}{10}\))

MN GIÚP MK NHA!

Answer 1

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\(A=\left(1-\frac{1}{3}\right)\left(1-\frac{1}{5}\right)\left(1-\frac{1}{7}\right)\left(1-\frac{1}{9}\right)\left(1-\frac{1}{11}\right)\left(1-\frac{1}{2}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{6}\right)\left(1-\frac{1}{8}\right)\left(1-\frac{1}{10}\right)\)

\(A=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{11}\right)\)

\(A=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot...\cdot\frac{10}{11}\)

\(A=\frac{1\cdot2\cdot3\cdot...\cdot10}{2\cdot3\cdot4\cdot...\cdot11}=\frac{1}{11}\)