\(C=4.5.6+5.6.7+...+\left(n-1\right).n.\left(n+1\right)\\ \Rightarrow4C=4.5.6.4+5.6.7.4+...+\left(n-1\right).n.\left(n+1\right).4\\ \Rightarrow4C=4.5.6.\left(7-3\right)+5.6.7.\left(8-4\right)+...+\left(n-1\right).n.\left(n+1\right).\left[\left(n+2\right)-\left(n-2\right)\right]\\ \Rightarrow C=4.5.6.7-3.4.5.6+5.6.7.8-4.5.6.7+...+\left(n-1\right).n.\left(n+1\right).\left(n+2\right)-\left(n-2\right).\left(n-1\right).n.\left(n+1\right)\\ \Rightarrow4C=\left(n-1\right).n.\left(n+1\right).\left(n+2\right)-3.4.5.6\\ \Rightarrow C=\frac{\left(n-1\right).n.\left(n+1\right).\left(n+2\right)-3.4.5.6}{4}\)
