Results 1 to 3 of 3

Thread: difficulty to simplyfy a sum expression

  1. #1
    Junior Member
    Joined
    Jul 2008
    From
    Athens, Greece
    Posts
    48

    Smile difficulty to simplyfy a sum expression

    Hello,

    I am trying to find the sum of a sequence, the problem is already solved in the book but not in a detailed way. While I understand the sum calculation process I don't understand the simplification result. I have marked in red the difference in the solution. In particular it says:

    etc etc
    Sum =
    (na/2) - (a/2)*(g^1 + g^2 + ... + g^n) + (nb/2) + (b/2)*(g^1 + g^2+ ... + g^n) =

    =(n/2)(a+b) + [(1-g^n)/(1-g)]*[(b-a)/2]
    the end

    My result is this:
    etc etc
    =(n/2)(a+b) + [(g-g^n+1)/(1-g)]*[(b-a)/2]
    the end

    I thought it could be some error, but there is the same result in an older version of the book. It might be something easy but still I cannot configure it out.

    Thank you all in advance,
    Melsi
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    10
    If you have transcribed this correctly then you are right and the book is wrong.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jul 2008
    From
    Athens, Greece
    Posts
    48

    solved: thank you

    Thank you very much for your kind a quick reply! It's of help to have a second opinion.
    I double checked again that I have write correctly the book's solution here...I worked on it a lot and I am coming to same conclusion as you did:

    The particular section, how solved it (very detailed):
    (g^1 + g^2 + ... + g^n) =
    [(...)*(1-g)] / [1-g] =
    [(...)(1) + (...)(-g)] / [...] =
    [(...) + (-1)(g)(...)] / [...] =
    [(...) + (-1)(g^2 + g^2 +...+g^n + g^n+1)] / [...] =
    [(...) + (-g^2 - g^3 - ... -g^n - g^n+1)] / [...]=
    [g^1 + g^2 + ... + g^n -g^2 -g^3-...-g^n -g^n+1] / [...]=
    [g^1 -g^n+1] / [1-g] or [g -g^n+1] / [1-g] .

    Thank you Plato,
    [If you haven't done already I would suggest you read the Socrates apology saved-written by Plato! Socrates reasoning, the way he acts in the court is exceptional.]
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Simplyfy this!
    Posted in the Algebra Forum
    Replies: 4
    Last Post: Mar 23rd 2011, 08:27 AM
  2. simplyfy the following as much as possible
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Apr 2nd 2009, 10:03 AM
  3. Replies: 3
    Last Post: Feb 21st 2009, 08:31 AM
  4. difficulty with one-to-ones
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Feb 3rd 2009, 06:38 PM
  5. Having a little difficulty
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: Jun 12th 2006, 05:47 PM

Search Tags


/mathhelpforum @mathhelpforum