1*2 + 2*3 + 3*4 + ...+ n*(n+1) = (1²+1) + (2²+2) + (3²+3) + ...+ (n²+n) = (1²+2²+3²+...+n²) + (1+2+3+...+n) = n(n+1)(2n+1)/6 + n(n+1)/2 = [n(n+1)/6] * (2n+1+3) ...