Results 1 to 2 of 2

Math Help - Show

  1. #1
    Super Member
    Joined
    Dec 2009
    Posts
    755

    Show

    Show that (\frac{1}{2})[\frac{(-3)(-4)...(-3-n+1)}{n!}(-\frac{1}{2})^n]=(\frac{1}{2})^{n+2}(n+1)(n+2)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Oct 2010
    From
    Mumbai, India
    Posts
    203

    Re: Show

    start taking -1 out from the left side

    (-1)^n\frac{1}{2}\left[\frac{(3)(4)\cdots(3+n-1)}{n(n-1)\cdots 2.1}\right]\left[-\frac{1}{2}\right]^n

    since there are total n terms in the numerator, we get a factor of (-1)^n
    out

    (-1)^{2n}\left[\frac{1}{2}\right]^{n+1}\frac{(3)(4)\cdots(n+2)}{n(n-1)\cdots  4.3.2.1}\right]

    ((-1)^2)^n\left[\frac{1}{2}\right]^{n+1}\frac{(3)(4)\cdots n(n+1)(n+2)}{n(n-1)\cdots  4.3.2.1}\right]

    now do the cancellations

    ((-1)^2)^n\left[\frac{1}{2}\right]^{n+1}\frac{(n+1)(n+2)}{2.1}\right]

    \left[\frac{1}{2}\right]^{n+2}(n+1)(n+2)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Show that
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: March 8th 2011, 01:05 PM
  2. show the way
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 14th 2009, 05:47 AM
  3. how to show show this proof using MAX
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 14th 2009, 01:05 PM
  4. How to show...
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 9th 2008, 10:07 AM
  5. how to show -u = (-1) u ?
    Posted in the Geometry Forum
    Replies: 1
    Last Post: May 21st 2008, 06:46 AM

/mathhelpforum @mathhelpforum