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Homework Help: Factorial simplifying

  1. Dec 7, 2008 #1
    1. The problem statement, all variables and given/known data

    I'm trying to prove k*(k!)=(k+1)!-1

    2. Relevant equations



    3. The attempt at a solution
    This is how far I've gotten:
    k[k(k-1)(k-2)....1)]
     
  2. jcsd
  3. Dec 7, 2008 #2
    What you are trying to prove is not true for all k.
     
  4. Dec 7, 2008 #3
    Ok, but then what would I do since I know it's true for k=1
     
  5. Dec 7, 2008 #4
    Are you sure the question doesn't say k * k! = (k + 1)! - k!?
     
  6. Dec 7, 2008 #5
    No, I'm positive. Just checked in the book.
     
  7. Dec 7, 2008 #6
    Plug in k = 2 to see that it's false.
     
  8. Dec 7, 2008 #7
    Ok, so if I was given this question. I just write only true for k=1?
     
  9. Dec 7, 2008 #8
    Well it's 1*1!+2*2!+...+k*k!=(k + 1)! - k!
     
  10. Dec 7, 2008 #9
    That's not true.

    [tex]k * k! = (k + 1 - 1) k! = (k + 1) k! - 1 * k! = (k + 1)! - k![/tex]
     
  11. Dec 7, 2008 #10
    1*1!+2*2!+...+k*k!=(k + 1)! - 1
    sorry...
     
  12. Dec 7, 2008 #11
    Okay, so how do you plan to prove this?
     
  13. Dec 7, 2008 #12
    Never mind. Just figured it out!
     
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