Results 1 to 3 of 3

Math Help - Few homework questions I'm having trouble with.

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    40

    Few homework questions I'm having trouble with.

    Assuming that the series is geometric, find the sum (correct up to 8 decimal places) of the first 25 terms of the following series:
    1-\frac{1}{2}+\frac{1}{4}-...

    Thanks

    jpatrie
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Apr 2008
    Posts
    1,092
    The sum of a geometric series through the first n terms, if the first term is one, is \frac{1 - r^n}{1 - r}, where r is the common ratio. In your example, r = -1/2. So the sum is \frac{1 - (-\frac{1}{2})^{25}}{1 + \frac{1}{2}}.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,337
    Thanks
    1247
    Quote Originally Posted by jpatrie View Post
    Assuming that the series is geometric, find the sum (correct up to 8 decimal places) of the first 25 terms of the following series:
    1-\frac{1}{2}+\frac{1}{4}-...

    Thanks

    jpatrie

    It is geometric. The common ratio is -\frac{1}{2}. Since |r|<1, it is also an infinite geometric series... but that's another story. a=1.

    The formula for sum of a geometric sequence is

    S_n = \frac{a(1-r^n)}{1-r}.

    We want the sum of the first 25 terms... so we have

    S_{25} = \frac{1\left(1 - \left(-\frac{1}{2})^{25}\right)\right)}{1-\left(-\frac{1}{2}\right)} = \frac{1 + \frac{1}{2^{25}}}{\frac{3}{2}}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Having trouble with these two questions!
    Posted in the Algebra Forum
    Replies: 12
    Last Post: October 10th 2010, 10:52 PM
  2. Some homework questions
    Posted in the Algebra Forum
    Replies: 2
    Last Post: December 3rd 2009, 06:18 PM
  3. Geometry homework trouble! Finding area....
    Posted in the Geometry Forum
    Replies: 3
    Last Post: April 22nd 2009, 07:54 PM
  4. Trouble with homework problem
    Posted in the Pre-Calculus Forum
    Replies: 9
    Last Post: March 14th 2009, 11:50 AM
  5. Textbook questions i had trouble with
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: April 11th 2008, 11:00 PM

Search Tags


/mathhelpforum @mathhelpforum