G4.4 If $W=2006^{2}-2005^{2}+2004^{2}-2003^{2}+\ldots+4^{2}-3^{2}+2^{2}-1^{2}$, find the value of $W$.
$\begin{aligned} W & =(2006+2005)(2006-2005)+(2004+2003)(2004-2003)+\ldots+(4+3)(4-3)+(2+1)(2-1) \\ & =2006+2005+2004+\ldots+4+3+2+1 \\ & =\frac{2006}{2}(2006+1)=1003 \times 2007=2013021\end{aligned}$