Question

Tính A=\(\left(\frac{1}{2}-1\right)\).\(\left(\frac{1}{3}-1\right)\)............\(\left(\frac{1}{2009}-1\right)\)

 

Answer 1

\(A=\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)...\left(\frac{1}{2009}-1\right)\)

\(A=\frac{-1}{2}\cdot\left(-\frac{2}{3}\right)\cdot\left(-\frac{3}{4}\right)\cdot\cdot\cdot\left(-\frac{2008}{2009}\right)\)

\(A=\frac{\left(-1\right)\left(-2\right)\left(-3\right)....\left(-2008\right)}{1.2.3.......2009}\)

\(A=\frac{\left(1.2.3......2008\right)}{\left(1.2.3......2008\right).2009}=\frac{1}{2009}\)