Use mathematical induction to prove that n(n+5) is divisible by 2 for any positive integer n.

Explanation:

We can deduce from the formula that any result from a positive integer for n will be divisible by 2, because of the following facts.

If n is an odd number, then n+5 will equal an even number. Also since an even number multiplied by an odd number equals an even number it is thereby divisible by 2.

Example: 3(3+5) ⇒ 3(8) = 24 (divisible by 2)

If n is an even number, then n+5 will equal an odd number, and as stated above any integer multiplied by an even number will equal an even number thus making it divisible by 2.

Example: 2(2+5) ⇒ 2(7) = 14 (divisible by 2)

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