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The coefficient of $x^{n}$ in the expansion of $(1 + x) (1 - x)^{n}$

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(−1)nn

(−1)n(1−n)

(−1)n−1(n−1)

(n−1)

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detailed solution

Correct option is B

(1+x)(1−x)n=[2−(1−x)](1−x)n =2(1−x)n−(1−x)n+1 ∴coefficient of xn in (1+x)(1−x)n=2(−1)n−n+1Cn(−1)n=(−1)n(2−n−1)=(−1)n(1−n)

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The coefficient of xn in the expansion of (1+x)(1−x)n

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The coefficient of $x^{n}$ in the expansion of $(1 + x) (1 - x)^{n}$