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
\[
\begin{array}{l}
2 C_{0}+2^{2} \frac{C_{1}}{2}+2^{3} \frac{C_{2}}{3}+2^{4} \frac{C_{3}}{4} \\
+\ldots \ldots 2^{n+1} \frac{C_{n}}{n+1}=\frac{3^{n+1}-1}{n+1}
\end{array}
\]
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