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Prove that n^5/5 + n^3/3+(7n)/(15) is a...

Prove that `n^5/5 + n^3/3+(7n)/(15)` is a natural number.

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To prove that \( P(n) = \frac{n^5}{5} + \frac{n^3}{3} + \frac{7n}{15} \) is a natural number for all natural numbers \( n \), we will use the principle of mathematical induction. ### Step 1: Base Case First, we check the base case for \( n = 1 \). \[ P(1) = \frac{1^5}{5} + \frac{1^3}{3} + \frac{7 \cdot 1}{15} \] ...
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