\(A=\left(1+\frac{1}{2003}\right).\left(1-\frac{1}{2004}\right).\left(1+\frac{1}{2005}\right).\left(1-\frac{1}{2006}\right).\left(1+\frac{1}{2007}\right).\left(1-\frac{1}{2008}\right)\)
\(=\frac{2004}{2003}.\frac{2003}{2004}.\frac{2006}{2005}.\frac{2005}{2006}.\frac{2008}{2007}.\frac{2007}{2008}\)
\(=1\)