Find the infinite Sum of the series with general term $\frac{1}{n(n+1)(n+2)}$.

I decomposed the fraction upto this $1/(2n)-1/(n+1)+1/(2n+4)$. But I find no link about cancelling terms. So how should I find the infinite Sum? 

Please don't say that this is off topic or homework. if wanna say that this is homework, at least give a hint if I am going the right way?