If \( (1+x)^{n}=C_{0}+C_{1} x+C_{2} x^{2}+\cdots+C_{n} x^{n}, n \in N \), then \( C_{0}-C_{1}+C_...
If \( (1+x)^{n}=C_{0}+C_{1} x+C_{2} x^{2}+\cdots+C_{n} x^{n}, n \in N \), then \( C_{0}-C_{1}+C_{2}-\cdots+(-1)^{m-1} C_{m-1} \) is equal to \( (mn) \)
(1) \( \frac{(n-1)(n-2) \cdots(n-m+1)}{(m-1) !}(-1)^{m-1} \)
(2) \( { }^{n-1} C_{m-1}(-1)^{m-1} \)
(3) \( \frac{(n-1)(n-2) \cdots(n-m)}{(m-1) !}(-1)^{m-1} \)
(4) \( { }^{n-1} C_{n-m}(-1)^{m-1} \)
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