If (1+x)^ =C_ n +C_ 1 x+C_ 2 x^ 2 + +C_ n x^ n , then for odd n, c_ 1 ^ 2 +c_ 3 ^ 2 +c_ 5…
Mathematics · JEE Main · NTA Exams — Binomial Theorem And Its Simple Applications
If \((1+x)^{\prime \prime}=C_{n}+C_{1} x+C_{2} x^{2}+\ldots+C_{n} x^{n}\), then for odd n, \(c_{1}^{2}+c_{3}^{2}+c_{5}^{2}+\ldots+c_{n}^{2}\) is equal to
- \(z^{2 n-2}\)
- \(2^{n}\)
- \(\frac{(2 n)!}{2(n!)^{2}}\)
- \(\frac{(2 n)!}{(n!)^{2}}\)
Answer
(D) (2 n)! (n!)^ 2
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