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

Explanation

To find the coefficient of \( x^n \) in the expansion of \( (1+x)(1-x)^n \), we can follow these steps:

### Step 1: Expand \( (1-x)^n \)
Using the Binomial Theorem, the expansion of \( (1-x)^n \) is given by:
\[ (1-x)^n = \sum_{k=0}^{n} \binom{n}{k} (-x)^k = \sum_{k=0}^{n} \binom{n}{k} (-1)^k x^k \]
This means that the coefficient of \( x^k \) in \( (1-x)^n \) is \( \binom{n}{k} (-1)^k \).
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