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Mathematical Induction simplification

  1. Mar 29, 2007 #1
    1. The problem statement, all variables and given/known data

    I have been workin on a mathematical induction question and have run into trouble with the simplification.

    2. Relevant equations

    3. The attempt at a solution

    I know that the solution i am trying to reach is (k+2)!-1
    but i do not know where to go from the equation:
    (k+1)!-1 + (k+1)(k+1)! could someone plz help.
  2. jcsd
  3. Mar 29, 2007 #2
    rearrange - put the -1 at the end and then look closely at the two terms now together.

    If you require more help please show what you have tried.
  4. Mar 29, 2007 #3


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    Homework Helper

    if in doubt always write out what the factorial really means
  5. Mar 29, 2007 #4


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    Homework Helper

    Try to factor out (k + 1)!, and see if you can get the answer. Note that:
    (n + 1) n! = (n + 1)!
    Can you go from here? :)
  6. Mar 29, 2007 #5
    (k+1)!-1 + (k+1)(k+1)!= (k+1)!+(k+1)(k+1)!-1, so here as the
    others explained you need to factor out (k+1)!, so you will get
    (k+1)!(1+k+1)-1=(k+2)(k+1)!-1, so now look at what vietdao said, and you will come to the right answer.
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