If $n \geq 100$ and the coefficient of $x^{100}$ in $1+(1+x)+(1+x)^2+\cdots+(1+x)^n$ is ${ }^{201} C_{101}$, then $n=$

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If $n \geq 100$ and the coefficient of $x^{100}$ in $1+(1+x)+(1+x)^2+\cdots+(1+x)^n$ is ${ }^{201} C_{101}$,…