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JEE MATHEMATICS MCQ: COMBINATIONS

1 Easy

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Application +4 | -1

If

n \ge 2

is a positive integer, then the sum of the series

^{n + 1}{C_2} + 2{(^2}{C_2}{ + ^3}{C_2}{ + ^4}{C_2} + ...{ + ^n}{C_2})

is

View answer and explanation

Correct option: B

\frac{{n\,(n + 1)\,\,(2n + 1)}}{6}

Option B (

\frac{{n\,(n + 1)\,(2n + 1)}}{6}

) is the correct sum of the series, derived using combinatorial identities and simplification.

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n