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Algebra problem ordinary numbers

  1. Jun 8, 2012 #1
    http://www.wolframalpha.com/input/?i=(k+1)!(k+2)+-1

    Could anyone explain how you get from (k+1)!(k+2) - 1 to (k+2)! - 1

    step by step please, here is my attempts:

    (k+1)k!(k+2) - 1
    (k+1)(k+2)k! - 1
    (k+1)(k+2)! -1
    no idea where to go from here
     
  2. jcsd
  3. Jun 8, 2012 #2

    Mark44

    Staff: Mentor

    This is very straightforward. (k + 2)! = (k + 2)*(k + 1)!
     
  4. Jun 8, 2012 #3
    how? isn't (k+2)*(k+1)k!? how is that (k+2)!?
     
  5. Jun 8, 2012 #4

    Mark44

    Staff: Mentor

    Isn't (k+2)*(k+1)k! what?
    (k + 2)! = (k + 2)*(k + 1)! = (k + 2) * (k + 1) * k!

    Let's look at ordinary numbers.

    8! = 8 * 7! = 8 * 7 * 6!
    = 8 * 7 * (6 * 5 * 4 * 3 * 2 * 1)
    = 56 * 720 = 40320
     
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