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