If (1+x)^ n = ^ n C_ n + ^ n C_ 1 x+ ^ n C_ 2 x^ 2 + + ^ n C_ n x^ n where, ^ n C_ n , ^…
Mathematics · JEE Main · NTA Exams — Binomial Theorem And Its Simple Applications
If \((1+x)^{n}={ }^{n} C_{n}+{ }^{n} C_{1} x+{ }^{n} C_{2} x^{2}+\ldots+{ }^{n} C_{n} x^{n}\) where, \({ }^{n} C_{n},{ }^{n} C_{1},{ }^{n} C_{2}, \ldots\)
are binomial coefficients and n is multiple of 3, then \(2\left[C_{4}+C_{3}+C_{5}+\ldots\right]+\left[C_{1}+C_{4}+C_{7}+\ldots\right](1+\omega)+\left[C_{2}+C_{5}+C_{4}+\ldots\right]\left(1+\omega^{2}\right)\) where ω is cube root of unity
- \(z^{n}+1\)
- \(z^{n-1}+1\)
- \(z^{n+1}-1\)
- \(z^{n}-1\)
Answer
(D) z^ n -1
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