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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 _…

Q1

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, 24 Feb (Shift 2)]

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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