Word Count : 382

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We will prove the given expression is a natural number for all \( n \in \mathbb{N} \) using mathematical induction. ### Step 1: Base Case \( n = 1 \) Substituting \( n = 1 \) in the given expression: \[ P(1) = \frac{1^5}{5} + \frac{1^3}{3} + \frac{7(1)}{15} \] \[ = \frac{1}{5} + \frac{1}{3} + \frac{7}{15} \] Finding the LCM of 5, 3, ____ __________ __________ ___ _____ ______ ________.
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