JEE Math Practice Question

If $$n \ge 2$$ is a positive integer, then the sum of the series $${}^{n + 1}{C_2} + 2\left( {{}^2{C_2} + {}^3{C_2} + {}^4{C_2} + ... + {}^n{C_2}} \right)$$ is :

1. A.$${{n(2n + 1)(3n + 1)} \over 6}$$
2. B.$${{n(n + 1)(2n + 1)} \over 6}$$
3. C.$${{n{{(n + 1)}^2}(n + 2)} \over {12}}$$
4. D.$${{n(n - 1)(2n + 1)} \over 6}$$