(n+1)(n+2)/1 +(n+2)(n+3)/1 +(n+3)(n+4)/1=(n+1)(n+2) +(n+2)(n+3) +(n+3)(n+4)=(n+2)(n+1+n+3)+n^2+7n+12=(n+2)(2n+4)+n^2+7n+12=2(n+2)^2+n^2+7n+12=2(n^2+4n+4)+n^2+7n+12=3n^2+15n+20