If $n \geq 2$ is a positive integer, then the sum of the series ${ }^{ n +1} C _{2}+2\left({ }^{2} C _{2}+{ }^{3} C _{2}+{ }^{4} C _{2}+\ldots+{ }^{ n } C _{2}\right)$ is ...... .
If $n \geq 2$ is a positive integer, then the sum of the series ${ }^{ n +1} C _{2}+2\left({ }^{2} C _{2}+{ }^{3} C _{2}+{ }^{4} C _{2}+\ldots+{ }^{ n } C _{2}\right)$ is ...... .
- [JEE MAIN 2021]
- A
$\frac{ n ( n -1)(2 n +1)}{6}$
- B
$\frac{ n ( n +1)(2 n +1)}{6}$
- C
$\frac{ n (2 n +1)(3 n +1)}{6}$
- D
$\frac{ n ( n +1)^{2}( n +2)}{12}$
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