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If $n$ is a positive integer and $f(n)$ is the coefficient of $x^n$ in the expansion of $(1+x)(1-x)^n$, then $f(2023)=$
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$2022$
$(1+x)(1-x)^{\mathrm{n}}$
$\begin{aligned} & \text { Coefficient of } x^n=1 \times \text { coefficient of } x^n \text { in }(1-x)^n \\ & +1 \times \text { coefficient of } x^{n-1} \text { in }(1-x)^n \\ & =(-1)^n \cdot{ }^n C_n+(-1)^{n-1} \cdot{ }^n C_{n-1}=(-1)^n+(-1)^{n-1} \cdot n \\ & \therefore f(n)=(-1)^n+(-1)^{n-1} \cdot n \\ & f(2023)=(-1)^{2023}+(-1)^{2022} \cdot 2023 \\ & =-1+2023=2022\end{aligned}$
$\begin{aligned} & \text { Coefficient of } x^n=1 \times \text { coefficient of } x^n \text { in }(1-x)^n \\ & +1 \times \text { coefficient of } x^{n-1} \text { in }(1-x)^n \\ & =(-1)^n \cdot{ }^n C_n+(-1)^{n-1} \cdot{ }^n C_{n-1}=(-1)^n+(-1)^{n-1} \cdot n \\ & \therefore f(n)=(-1)^n+(-1)^{n-1} \cdot n \\ & f(2023)=(-1)^{2023}+(-1)^{2022} \cdot 2023 \\ & =-1+2023=2022\end{aligned}$
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