Results 1 to 8 of 8

Math Help - simplify (factorial expression)

  1. #1
    Newbie
    Joined
    Nov 2011
    Posts
    11

    simplify (factorial expression)

    x! - [(x-1)!+(x-2)!+(x-3)!...............2!+1!]
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Aug 2011
    Posts
    127

    Re: simplify (factorial expression)

    Intuitive guess, based on 5:
    expression is 5*4*3*2*1 - 4*3*2*1 - 3*2*1 - 2*1 - 1 = 4*4*3*2*1 - 3*2*1 - 2*1 - 1 = 4*3*2*2*1 etc.

    So I think the answer is going to be (x-1)!, though that's not a formal proof.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,393
    Thanks
    1476
    Awards
    1

    Re: simplify (factorial expression)

    Quote Originally Posted by Annatala View Post
    Intuitive guess, based on 5:
    expression is 5*4*3*2*1 - 4*3*2*1 - 3*2*1 - 2*1 - 1 = 4*4*3*2*1 - 3*2*1 - 2*1 - 1 = 4*3*2*2*1 etc.
    So I think the answer is going to be (x-1)!, though that's not a formal proof.
    5! - \left( {\sum\limits_{k = 1}^4 {(5 - k)!} } \right) = 87.

    If E_N=N! - \left( {\sum\limits_{k = 1}^{N-1} {(N - k)!} } \right) for N\ge 2 then we get 1,~3,~15,~87,~567 for the first five of those.

    I have not seen a pattern yet.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,417
    Thanks
    718

    Re: simplify (factorial expression)

    See also the MathWorld article on the sum of factorials.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,393
    Thanks
    1476
    Awards
    1

    Re: simplify (factorial expression)

    Quote Originally Posted by emakarov View Post
    See also the MathWorld article on the sum of factorials.
    Also looking at this sequence site we see that this does not to yield much.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Nov 2011
    Posts
    11

    Re: simplify (factorial expression)

    do v have any other expression for sum of factorial ??

    may be we can find a range (in terms of n) in which the answer would lie..

    I ll try this now...
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,393
    Thanks
    1476
    Awards
    1

    Re: simplify (factorial expression)

    Quote Originally Posted by livinggourmand View Post
    do v have any other expression for sum of factorial ??
    may be we can find a range (in terms of n) in which the answer would lie..I ll try this now...
    I have no idea what that post says.
    If you follow the link in post #5, it is clear that the folks at ATT labs do not know of any simplification of this sequence.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Member
    Joined
    Aug 2011
    Posts
    127

    Re: simplify (factorial expression)

    Ah, I figured out the mistake in my quickie guess-calculation.

    a * b * c - b * c = (a-1) * b * c is true, but a * b * c - c = (a * (b-1) * c) is false. It should = ((a * b) - 1) * c, which doesn't simplify and gets worse the longer the expression is.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Simplify the factorial expression
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: September 27th 2009, 03:37 AM
  2. Simplify a factorial
    Posted in the Algebra Forum
    Replies: 5
    Last Post: September 22nd 2008, 06:17 AM
  3. Simplify Expression
    Posted in the Trigonometry Forum
    Replies: 9
    Last Post: May 9th 2008, 02:35 PM
  4. help me to simplify this factorial
    Posted in the Algebra Forum
    Replies: 2
    Last Post: July 16th 2007, 09:18 AM
  5. simplify expression
    Posted in the Algebra Forum
    Replies: 1
    Last Post: April 22nd 2007, 05:09 PM

Search Tags


/mathhelpforum @mathhelpforum