By induction, prove that : \( 1.2+2 \cdot 3+3 \cdot 4+\ldots+(n-1) ...

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By induction, prove that :
\( 1.2+2 \cdot 3+3 \cdot 4+\ldots+(n-1) n=\frac{(n-1) n(n+1)}{3} \), for all natural numbers \( n, n \geq 2 \).
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