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Taylor series (doing something wrong!) watch

    • Thread Starter


    the question first asks me to find the taylor expansion of 1/(1-x) by differentiating successively at x=0.

    I've done that and obtained the following: 1 + x + x2 + x3 + .......

    This is the next part of the question:

    b) Use this to find the Taylor expansion for arctan z about z=0 (Hint: recall d/dz (arctan z) = 1/ (1+ z2) and so substitute x= -z2 into the expansion of part a.)

    I've substitued x=... into my first expansion but I get: 1 - z2- z4- ........

    I know this is not right, because I've done it the long way, but what am I doing wrong?

    Thanks in advance.

    d/dz(arctan z)=1/(1+z^2)

    Let x = -z^2

    and you get 1 - z^2 + z^4-... from part a) which is where youre going wrong by the looks of it.

    Then integrate term by term to get

    arctan z = z -1/3z^3+ 1/5z^5

    No problem
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Updated: October 16, 2006

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