If \( n \geq 2 \) is a positive integer, then the sum of the series \( \mathrm{P} \) \( { }^{n+1...

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If \( n \geq 2 \) is a positive integer, then the sum of the series
\( \mathrm{P} \) \( { }^{n+1} C_{2}+2\left({ }^{2} \mathrm{C}_{2}+{ }^{3} \mathrm{C}_{2}+{ }^{4} \mathrm{C}_{2}+\ldots+{ }^{n} \mathrm{C}_{2}\right) \) is:

W
[JEE Main-2021 (February)]
(a) \( \frac{n(n+1)^{2}(n+2)}{12} \)
(b) \( \frac{n(n-1)(2 n+1)}{6} \)
(c) \( \frac{n(n+1)(2 n+1)}{6} \)
(d) \( \frac{n(2 n+1)(3 n+1)}{6} \)
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