Prove that n2-n is even for every positive integer n.


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Answer:


Step by Step Explanation:
  1. We have been asked to prove that n2 - n is even for every positive integer n.
  2. Before beginning, we have to understand the following
    Even × Even = Even
    Even - Even = Even
    Odd - Odd = Even
    Odd × Odd = Odd
  3. First, suppose n is odd:
    Now, n2 - n = (odd)2 - (odd)
    = odd × odd - odd
    = odd - odd
    = Even
  4. Second, suppose n is even:
    Now, n2 - n = (even)2 - (even)
    = even × even - even
    = even - even
    = even
  5. Therefore, n2 - n is even for every positive integer n.

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