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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
\[
\begin{array}{l}
3 .{ }^{n} C_{1}+7 \cdot{ }^{n} C_{2}+11 \cdot{ }^{n} C_{3}+\ldots+(4 n-1) \cdot{ }^{n} C_{n}=(2 n-1) 2^{n} \\
+1
\end{array}
\]
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