If \( (1+x)^{n}=C_{0}+C_{1} x+C_{2} x^{2}+C_{3} x^{3}+C_{n} x^{n} \...

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If \( (1+x)^{n}=C_{0}+C_{1} x+C_{2} x^{2}+C_{3} x^{3}+C_{n} x^{n} \), prove
\( \mathrm{P} \)
that
W
\[
5 C_{1}+9 C_{2}+13 C_{3}+\ldots .+(4 n+1) C_{n}=(2 n+1) 2^{n}-1
\]
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