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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
\[
\begin{array}{l}
\frac{C_{0}}{2}-\frac{C_{1}}{3}+\frac{C_{2}}{4}-\frac{C_{3}}{5}+\ldots .+(-1)^{n} \cdot \frac{C_{n}}{n+2} \\
=\frac{1}{(n+1)(n+2)}
\end{array}
\]
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