Prove by the principle of mathematical induction that `(n^5)/5+(n^3)/3+(7n)/(15)` is a natural number for all `n in Ndot`

Explanation

To prove that \( \frac{n^5}{5} + \frac{n^3}{3} + \frac{7n}{15} \) is a natural number for all \( n \in \mathbb{N} \) using the principle of mathematical induction, we will follow these steps:

### Step 1: Base Case
We start by checking the base case, \( n = 1 \).

\[ P(1) = \frac{1^5}{5} + \frac{1^3}{3} + \frac{7 \cdot 1}{15} \]
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