Results 1 to 5 of 5

Math Help - power series?

  1. #1
    Newbie
    Joined
    May 2008
    Posts
    11

    power series?

    Man, this class is horrible. I just got a 56 on the midterm and it was one of the top scores in the class since the average is a 40. The book is so unhelpful...they give us some general examples and theories and then bombard us with dozens of questions far more advanced than any of the info they give us. Anyway, enough of a rant, onto my question. I am working on a similar problem to this one. I understand how they get the derivative but have no idea how they go from there to the final solution. This is from our solutions manual which gives us the odd-numbered answers. The step I don't understand is followed by ???.

    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by CrazyLond View Post
    Man, this class is horrible. I just got a 56 on the midterm and it was one of the top scores in the class since the average is a 40. The book is so unhelpful...they give us some general examples and theories and then bombard us with dozens of questions far more advanced than any of the info they give us. Anyway, enough of a rant, onto my question. I am working on a similar problem to this one. I understand how they get the derivative but have no idea how they go from there to the final solution. This is from our solutions manual which gives us the odd-numbered answers. The step I don't understand is followed by ???.

    WEll first off there is a problem

    The index should read \sum_{{n=\color{red}{1}}}^{{\infty}}(-1)^nnx^{n-1}

    Then adjusting that down to zero we get,

    \sum_{n=0}^{\infty}(-1)^{n+1}(n+1)x^{n}

    This was just gotten through elementary index manipluation

    Now then using the root test we get the interval of convergence is equal to

    \lim_{n\to\infty}|(n+1)x^n|^{\frac{1}{n}}<1\Righta  rrow|x|<1

    Now putting in both x=1 and x=-1 we get divergence by the n-th term test
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2008
    Posts
    11
    I guess I'm weak on index manipulation.

    Looking closer, n=1 is what they had there. Why does it go from 0 to 1 in the first place? I guess I'll review the chapter on those things.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by CrazyLond View Post
    I guess I'm weak on index manipulation.

    Looking closer, n=1 is what they had there. Why does it go from 0 to 1 in the first place? I guess I'll review the chapter on those things.
    You tell me, look at the exponent of the x term in the power series, and report back
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    May 2008
    Posts
    11
    I guess we don't want a negative exponent? I guess that makes sense, thanks.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: September 29th 2010, 06:11 AM
  2. Replies: 0
    Last Post: January 26th 2010, 08:06 AM
  3. Formal power series & Taylor series
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: April 19th 2009, 09:01 AM
  4. Multiplying power series - Maclaurin series
    Posted in the Calculus Forum
    Replies: 4
    Last Post: March 7th 2009, 11:24 PM
  5. Replies: 10
    Last Post: April 18th 2008, 10:35 PM

Search Tags


/mathhelpforum @mathhelpforum