Factorisation?

Let S=n(n+1)(n+2)+n(n+1)(n+2)+....

for n=1 to n=2007

n(n+1)(n+2)= $n^3$ +3 $n^2$ +2n

Referring to wiki,

We would have

S= $\frac{(n^2)(n+1)^2}{4}$ +3[ $\frac{n(n+1)(2n+1)}{6}$ ]+2[ $\frac{n(n+1)}{2}$ ]

After simplifying,

4×S÷[n(n+1)(n+2)]

= $\frac{(n+1)(n+4)+2}{n+2}$

= $\frac{(2008)(2011)+2}{2009}$

= $\boxed{2010}$