4. Find the value of $\sum_{k=0}^{n-1} C_{2 n-1}^{k}$.

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4. From $C_{2 n-1}^{n}+C_{2 n-1}^{n+1}+C_{2 n-1}^{n+2}+\cdots+C_{2 n-1}^{2 n}+C_{2 n-1}^{2 n-1}=C_{2 n-1}^{n-1}+C_{2 n-1}^{n-2}+C_{2 n-1}^{n-3}+\cdots$ $+C_{2 n-1}^{1}+C_{2 n-1}^{0}$, we know that $\sum_{k=0}^{n-1} C_{2 n-1}^{k}=2^{2 n-2}$.