By using "Principle of Mathematical Induction", prove \( \mathrm{P}...

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By using "Principle of Mathematical Induction", prove
\( \mathrm{P} \) that for all \( n \in N \) :

W
\[
1^{2}+2^{2}+3^{2}+\ldots+n^{2}=\frac{n(n+1)(2 n+1)}{6}
\]
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