Show that \( \sum_{r=0}^{n} \frac{C_{r} \cdot 3^{r+4}}{(r+1)(r+2)(r+3)(r+4)} \) \[ -=\frac{1}{(n...

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Show that \( \sum_{r=0}^{n} \frac{C_{r} \cdot 3^{r+4}}{(r+1)(r+2)(r+3)(r+4)} \)
\[
-=\frac{1}{(n+1)(n+2)(n+3)(n+4)}\left[4^{n+4}-\sum_{s=0}^{3}{ }^{n+4} C_{s} \cdot 3^{s}\right]
\]
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