Prove that \( C_{0}{ }^{2}-C_{1}{ }^{2}+C_{2}{ }^{2}-C_{3}{ }^{2}+\ldots \ldots+(-1)^{n} C_{n}{ }^{2} \) \( =0 \) or \( (-1)^{n

Prove that \( C_{0}{ }^{2}-C_{1}{ }^{2}+C_{2}{ }^{2}-C_{3}{ }^{2}+\ldots \ldots+(-1)^{n} C_{n}{ }^{2} \) \( =0 \) or \( (-1)^{n / 2} C_{n / 2} \) according as \( n \) is odd or even.

Prove that \( C_{0}{ }^{2}-C_{1}{ }^{2}+C_{2}{ }^{2}-C_{3}{ }^{2}+\ldots \ldots+(-1)^{n} C_{n}{ }^{2} \) \( =0 \) or \( (-1)^{n / 2} C_{n / 2} \) according as \( n \) is odd or even.

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