Hi guys, I've been reading the forum for the past 2 semesters of school now and came across a question I couldn't find in the search.

I am to prove 1/1*2*3 +1/2*3*4 + 1/3*4*5 +...+ 1/n(n+1)(n+2) = n(n+3)/4(n+1)(n+2)

I am at solving the induction part, but am unable to do finish, I keep getting stuck on what seems to be moderate algebra and I don't know what to do next.

Thanks in advance!