Results 1 to 7 of 7

Math Help - Series help!

  1. #1
    Newbie
    Joined
    Jan 2009
    Posts
    21

    Series help!

    Hey folks.

    I still havent got my head round the idea of a series expansion and am stuck on the questions in my homework regard series expansion.

    1) What is the series expansion of ln(1+x^2 / 100) and it's radius of conversion?

    There is a an x-formula in my textbook which reads ln x = (x-1) - \frac{1}{2}(x-1)^2 + \frac{1}{3}(x-1)^3 - .... First of all I don't exactly understand where it has come from (the explanation isn't clear) and secondly, can I just plug in my "x" is into the formula?
    I know the Radius of Convergence is when the function doesn't make sense so for the question the ROC is infinity i.e. it always makes sense?


    2) Use the fact that  sin x = Im(exp(ix)) to calculate a simpler derivation of this result.

    Im not at all sure where to start...something to do with De Moivre's theorem I beleive but I've never really understood it? Could you point me in the right direction or more?

    Thanks a lot people
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by Solo View Post
    Hey folks.

    I still havent got my head round the idea of a series expansion and am stuck on the questions in my homework regard series expansion.

    1) What is the series expansion of ln(1+x^2 / 100) and it's radius of conversion?

    There is a an x-formula in my textbook which reads ln x = (x-1) - \frac{1}{2}(x-1)^2 + \frac{1}{3}(x-1)^3 - .... First of all I don't exactly understand where it has come from (the explanation isn't clear) and secondly, can I just plug in my "x" is into the formula?
    I know the Radius of Convergence is when the function doesn't make sense so for the question the ROC is infinity i.e. it always makes sense?
    see here under "List of Taylor series of some common functions" and find the formula for \ln (1 + x) (they write "log" instead of "ln" here). just replace x with \frac {x^2}{100} everywhere. it also show you how they derive it.

    you must review Taylor series and MacLauren series expansions.


    2) Use the fact that  sin x = Im(exp(ix)) to calculate a simpler derivation of this result.
    what result? the one in part (1)?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    o_O
    o_O is offline
    Primero Espada
    o_O's Avatar
    Joined
    Mar 2008
    From
    Canada
    Posts
    1,407
    Quote Originally Posted by Solo View Post
    2) Use the fact that  sin x = Im(exp(ix)) to calculate a simpler derivation of this result.
    How curious. The poster here posted the same problem with the same mistake: Series Expansion
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    The series for ln(1+t)=\sum_{n=1}^{\infty}\frac{(-1)^{t+1}t^{n}}{n}

    Try that.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jan 2009
    Posts
    21
    Thanks.

    Ah sorry it is related to another question which I forgot to post.

    (a) Find the first 4 terms in the power series expansion of  e^x sin x by multiplying together the series expanstions of  e^x and  sin x .

    (b) Use the fact that  sin x = Im(exp(ix)) to calculate a simpler derivation of this result.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by Solo View Post
    Thanks.

    Ah sorry it is related to another question which I forgot to post.

    (a) Find the first 4 terms in the power series expansion of  e^x sin x by multiplying together the series expanstions of  e^x and  sin x .

    (b) Use the fact that  sin x = Im(exp(ix)) to calculate a simpler derivation of this result.
    see the link given in post #3
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Jan 2009
    Posts
    21
    Yep. Thanks.
    Last edited by mr fantastic; January 25th 2009 at 07:18 PM. Reason: Deleting the trigger for the string of off-topic posts (that are now deleted)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: October 3rd 2011, 02:12 AM
  2. Replies: 3
    Last Post: September 29th 2010, 07:11 AM
  3. Replies: 0
    Last Post: January 26th 2010, 09:06 AM
  4. Replies: 2
    Last Post: December 1st 2009, 01:45 PM
  5. Replies: 1
    Last Post: May 5th 2008, 10:44 PM

Search Tags


/mathhelpforum @mathhelpforum