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 :
\( \mathrm{P} \) \( C_{0}-\frac{C_{1}}{\sqrt{2}}+\frac{C_{2}}{2}-\frac{C_{3}}{2 \sqrt{2}} \ldots \ldots . \). upto \( (n+1) \) terms equal to \( \left(1-\frac{1}{\sqrt{2}}\right)^{n} \)

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