1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Factorial simplifying
  1. Sum with factorial (Replies: 9)

  2. Factorial Sequences (Replies: 12)

Loading...