If \( C_{0}, C_{1}, C_{2}, \ldots C_{n} \) are the binomial coeffic...

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If \( C_{0}, C_{1}, C_{2}, \ldots C_{n} \) are the binomial coefficients in the expansion of \( (1+x)^{n} \) then prove that :
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\( -C_{1}(3)^{n-1}(\sqrt{5})^{1}+C_{2}(3)^{n-2} 5-C_{3} 3^{n-3}(5 \sqrt{5}) \) upto \( (n) \) terms equal to \( (3-\sqrt{5})^{n}-3^{n} \)
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