Using principle of mathematical induction prove that : \( \frac{n^{...

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Using principle of mathematical induction prove that :
\( \frac{n^{7}}{7}+\frac{n^{5}}{5}+\frac{2 n^{3}}{3}-\frac{n}{105} \) is an integer for all \( n \in \mathbf{N} \).
\( \mathrm{P} \)
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