Prove the following by using the principle of mathematical inductio...

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Prove the following by using the principle of mathematical induction for all \( n \in \mathbf{N} \) :
\[
1.2 .3+2.3 .4+\ldots+n(n+1)(n+2)=\frac{n(n+1)(n+2)(n+3)}{4} \text {. }
\]
\( \mathrm{P} \)
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