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Taylor Series Problem - Question and my attempt so far

  1. Jan 17, 2013 #1
    Question:

    http://i.imgur.com/GsjeL.png

    Here is my attempt so far:

    http://i.imgur.com/AyOCm.png

    Note: I've used m where the question has used j.

    My attempt is based off some bad notes I took in class so the way I am trying to solve the problem may not be the best. I'm struggling to work out how to continue from the part where I've left a question mark, and I'm not even sure if the Taylor expansion is correct.

    Could anybody offer some thoughts as to what to do?
     
  2. jcsd
  3. Jan 17, 2013 #2

    SammyS

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    Hello jammyloller. Welcome to PF !

    attachment.php?attachmentid=54821&stc=1&d=1358466852.png

    attachment.php?attachmentid=54817&stc=1&d=1358463969.jpg

    I'm not sure what your notes are supposed to say, but the Taylor expansion of f(x) about the point x0 is given by
    [itex]\displaystyle f(x)=f(x_0)+f'(x_0)\Delta x
    +\frac{f''(x_0)}{2!}(\Delta x)^2+\frac{f'''(x_0)}{3!}(\Delta x)^3+\frac{f''''(x_0)}{4!}(\Delta x)^4+\dots\ ,\ \ \text{ where }\ \ \Delta x=x-x_0\ .[/itex]​
     

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