Find the sum of $n$ terms of the series $1\times 2+2\times 3+3\times 4+4\times 5+.............$

Question

$\begin{array}{1 1} \large\frac{n(n+1)(n+2)}{3} \\ \large\frac{n(n+1)(n+2)}{6} \\ \large\frac{n(n+1)(2n+1)}{3} \\ \large\frac{n(n+1)(n+2)}{2} \end{array}$