Question

tìm x

\(\left(1-\frac{1}{2}\right)x\left(1-\frac{1}{3}\right)x\left(1-\frac{1}{4}\right)x.......x\left(1-\frac{1}{10}\right)=\frac{x}{2010}\)

Answer 1

\(\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right)\cdot...\cdot\left(1-\frac{1}{10}\right)=\frac{x}{2010}\)

\(\Leftrightarrow\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot...\cdot\frac{9}{10}=\frac{x}{2010}\)

\(\Leftrightarrow\frac{1\cdot2\cdot3\cdot....\cdot9}{2\cdot3\cdot4\cdot....\cdot10}=\frac{x}{2010}\)

\(\Leftrightarrow\frac{1}{10}=\frac{x}{2010}\)

\(\Leftrightarrow x=\frac{2010}{10}=201\)

Answer 2

Ta có : \(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)......\left(1-\frac{1}{10}\right)=\frac{x}{2010}\)

=> \(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}......\frac{9}{10}=\frac{x}{2010}\)

\(\Rightarrow\frac{1.2.3......9}{2.3.4.....10}=\frac{x}{2010}\)

\(\Rightarrow\frac{1}{10}=\frac{x}{2010}\)

\(\Rightarrow x=\frac{2010}{10}=201\)

\(=\frac{1}{10}\)