Question

Find the coefficient of \(x^n\) in the expansion of \((1+x)(1-x)^n\)

Answer 1

We have, 

Coefficient of \(x^n\) in \((1+x)(1-x)^n\)

= coefficient of \(x^n\) in \((1-x)^n\) + coefficient of \(x^{n-1}\) in \((1-x)^n\)

= \((-1)^n\) ⁿC_n+(-1)^n-1nC_n-1

=\((-1)^n(1-n)\)