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The coefficient of x^n in expansion of (1+x)(1-x)^n \text { is }

Option: 1

(-1)^{n-1} n


Option: 2

(-1)^n(1-n)


Option: 3

(-1)^{n-1}(n-1)^2


Option: 4

(n-1)


Answers (1)

best_answer

Coefficient of x^n  in expansion of (1+x)(1-x)^n ie., coefficient of x^{n} in expansion of (1-x)^n+ coefficient of x^{n-1} in expansion of (1-x)^n \text { Now, }(-1)^n{ }^n C_n+(-1)^{n-1}{ }^n C_{n-1} (-1)^n\left[{ }^n C_n-{ }^n C_{n-1}\right]=(-1)^n[1-n]

 

Posted by

Sanket Gandhi

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