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Interesting arithmetic sequence

  1. Jun 29, 2011 #1
    Given N= 1.2.3 + 2.3.4 + ... + n(n+1)(n+2), prove that 4N + 1 is a square (n is a positive integer)
     
  2. jcsd
  3. Jun 29, 2011 #2
    It's easy to see that (see www.math.uic.edu/~kauffman/DCalc.pdf on how to find such things)

    [tex]1.2.3+...+n(n-1)(n-2)=\frac{(n+1)n(n-1)(n-2)}{4}[/tex]

    Thus it suffices to show that

    [tex](n+1)n(n-1)(n-2)+1[/tex]

    is a square. Which is a much simpler problem.
     
  4. Jun 29, 2011 #3
    Great!
     
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