Results 1 to 4 of 4

Math Help - [SOLVED] Help agent!

  1. #1
    Mealea
    Guest

    Exclamation [SOLVED] Help agent!

    I can't solve this exercise,please help me.
    Calculate,
    S=1!+2!+3!..............+2006!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    I searched some math sites. It seems to me that there is no elegant solution. Your problem is based on something called the "left factorial".
    n\geq 1 we define,
    !n=(n-1)!+(n-2)!+...+2!+1!
    Then,
    !n=\left[ \frac{n!}{e} \right]
    Where, [ \, ] is the nearest interger function.
    Thus,
    1!+...+2006!=!2007
    And thus,
    1!+...+2006!=\left[ \frac{2007!}{e} \right]
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2005
    From
    Wethersfield, CT
    Posts
    92
    Hi Hckr:

    I don't get it. 4!/e rounds to 9, and 1! +2! + 3! = 9. Yea!

    1! + 2! = 3, but 3! / e rounds to 2.

    1! + 2! + 3! + 4! = 33, but 5!/e rounds to 44.

    Thanks in advance,

    Rich B.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Quick's Avatar
    Joined
    May 2006
    From
    New England
    Posts
    1,024

    A different approach...

    I'm not entirely sure if this shortens anything...

    We have a number x such that x=1!+2!...2005!+n! it can be rewritten as
    x=1+2(1(n-1)+ 3(n-2)+4(n-3)....2005(n-2004)+2006(n-2005))

    I can simplify further, but I'll let you guys decide the best method...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Multi-Agent Path Planning Optimization Problem.
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: April 14th 2010, 04:08 AM

Search Tags


/mathhelpforum @mathhelpforum