If C r stands for n C r , then the sum of the series 2 ( n 2 )! ( n 2 )! n! [C_ 0 ^ 2 -2…
Mathematics · JEE Advanced · NTA Exams — Binomial Theorem And Its Simple Applications
If Cr stands for nCr , then the sum of the series
\[\frac{2\left(\frac{n}{2}\right)!\left(\frac{n}{2}\right)!}{n!}\left[C_{0}^{2}-2 C_{1}^{2}+\ldots \ldots \ldots \ldots+(-1)^{n}(n+1) C_{n}^{2}\right]\]
where n is an even positive integer, is equal to
\[\frac{2\left(\frac{n}{2}\right)!\left(\frac{n}{2}\right)!}{n!}\left[C_{0}^{2}-2 C_{1}^{2}+\ldots \ldots \ldots \ldots+(-1)^{n}(n+1) C_{n}^{2}\right]\]
where n is an even positive integer, is equal to
- 0
- (–1)n/2 (n + 1)
- (–1)n (n + 2)
- none of these
Answer
(A) 0
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