The coefficient of $x^n$ in expansion of $(1+x)(1-x)^n$ is

The coefficient of $x^n$ in expansion of $(1+x)(1-x)^n$ is
  1. $(n-1)$
  2. $(-1)^n(1-n)$
  3. $(-1)^{n-1}(n-1)^2$
  4. $(-1)^{n-1} n$

Solution

Coefficient of $x^n$ in $(1+x)(1-x)^n=(1+x)\left({ }^n C_0-{ }^n C_1 x+\ldots \ldots .+(-1)^{n-1}{ }^n C_{n-1} x^{n-1}+(-1)^n\right.$ $\left.{ }^n C_n x^n\right)$ $=(-1)^n{ }^n C_n+(-1)^{n-1}{ }^n C_{n-1}=(-1)^n(1-n)$

Asked in: JEE Main 2004

Practice more Binomial Theorem questions on Aicharya