JEE Mains · Maths · STD 11 - 6. permutation and combination
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 ...... .
- 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 \(\frac{ n ( n +1)^{2}( n +2)}{12}\)
Answer & Solution
Correct Answer
(B) \(\frac{ n ( n +1)(2 n +1)}{6}\)
Step-by-step Solution
Detailed explanation
\({ }^{n+1} C_{2}+2\left({ }^{2} C_{2}+{ }^{3} C_{2}+{ }^{4} C_{2}+\ldots \ldots .+{ }^{n} C_{2}\right)\) \({ }^{n+1} C_{2}+2\left({ }^{3} C_{3}+{ }^{3} C_{2}+{ }^{4} C_{2}+\ldots \ldots .+{ }^{n} C_{2}\right)\) \(\left\{\right.\) use…
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