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prove that n(n^(2)+5) is divisible by 6,...

prove that `n(n^(2)+5)` is divisible by 6, for each natural number n.

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To prove that \( n(n^2 + 5) \) is divisible by 6 for each natural number \( n \), we will use the principle of mathematical induction. ### Step 1: Base Case We start by checking the base case, \( n = 1 \): \[ P(1) = 1(1^2 + 5) = 1(1 + 5) = 1 \times 6 = 6 \] Since 6 is divisible by 6, the base case holds. ...
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