Results 1 to 3 of 3

Math Help - Trouble calculating an alternating/infinite sum

  1. #1
    s3a
    s3a is offline
    Super Member
    Joined
    Nov 2008
    Posts
    597

    Trouble calculating an alternating/infinite sum

    Firstly, the sum is attached as a png file and the answer is that it converges (conditionally) to 1/12.

    I thought about the fact that I could split that up to two sums yielding one with all the positive terms and one with all the negative terms and then evaluate the sums separately and then have simple arithmetic at the end but I don't know how to set up the positive/negative separation. In other words, I don't know what needs to be done mechanically in order to transform that one infinite sum into two infinite sums (one being positive and the other negative).

    Any help would be greatly appreciated!
    Thanks in advance!

    Edit: If I am completely off in my reasoning, just please tell me how to do it in the first place.
    Attached Thumbnails Attached Thumbnails Trouble calculating an alternating/infinite sum-thesumimhavingtroublewith.png  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,863
    Thanks
    638

    Re: Trouble calculating an alternating/infinite sum

    Quote Originally Posted by s3a View Post
    Firstly, the sum is attached as a png file and the answer is that it converges (conditionally) to 1/12.

    I thought about the fact that I could split that up to two sums yielding one with all the positive terms and one with all the negative terms and then evaluate the sums separately and then have simple arithmetic at the end but I don't know how to set up the positive/negative separation. In other words, I don't know what needs to be done mechanically in order to transform that one infinite sum into two infinite sums (one being positive and the other negative).

    Any help would be greatly appreciated!
    Thanks in advance!

    Edit: If I am completely off in my reasoning, just please tell me how to do it in the first place.
    \sum_{n=1}^{\infty} \frac{(-4)^{n-1}}{8^n} = -\frac{1}{4} \cdot \sum_{n=1}^{\infty} \frac{(-4)^{n}}{8^n} = -\frac{1}{4} \cdot \sum_{n=1}^{\infty} \left(-\frac{1}{2}\right)^n

    sum of an infinite geometric series ...

    S = -\frac{1}{4} \cdot \frac{-\frac{1}{2}}{1 - \left(-\frac{1}{2}\right)}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    s3a
    s3a is offline
    Super Member
    Joined
    Nov 2008
    Posts
    597

    Re: Trouble calculating an alternating/infinite sum

    Thanks! I get it now !
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Infinite Series with Double Alternating Signs
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 9th 2011, 05:23 PM
  2. An Alternating Infinite Series
    Posted in the Math Challenge Problems Forum
    Replies: 10
    Last Post: January 26th 2011, 12:45 PM
  3. Trouble calculating residues
    Posted in the Calculus Forum
    Replies: 5
    Last Post: June 25th 2009, 08:07 AM
  4. Trouble calculating the scale function of a diffusion process
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: May 30th 2009, 08:21 AM
  5. Trouble calculating a confidence interval
    Posted in the Statistics Forum
    Replies: 1
    Last Post: April 15th 2009, 10:23 PM

Search Tags


/mathhelpforum @mathhelpforum