Question

​find the coefficient of xn in the expansion of(1+x)(1-x)n

Answer 1

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Coefficient of xn in (1+x)(1−x)n=1× coeff. of xn in (1−x)n+1× coeff. of xn−1 in (1−x)n

∴ Coefficient of xn in (1+x)(1−x)n=(−1)nnCn+(−1)n−1nCn−1

=(−1)n[1−n]