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Math Help - Taylor Series (check my answer plz)

  1. #1
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    Taylor Series (check my answer plz)

    Find the infinite Taylor Series representation for f(x) = cos(2x), centered
    at C = pi/4

    This is what I got, not too sure about the correctness of it haha.

    wish I knew how to write in that neat math font...anyway

    Summation of 0 to infinity = ((-1)*2^n)/((2n)!) * (x-(pi/4))^(2n)

    thanks.
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  2. #2
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    Quote Originally Posted by Grimey View Post
    Find the infinite Taylor Series representation for f(x) = cos(2x), centered
    at C = pi/4

    This is what I got, not too sure about the correctness of it haha.

    wish I knew how to write in that neat math font...anyway

    Summation of 0 to infinity = ((-1)*2^n)/((2n)!) * (x-(pi/4))^(2n)

    thanks.
    I get -2\bigl(x-\tfrac\pi4\bigr) + \frac{8\bigl(x-\tfrac\pi4\bigr)^3}{3!} - \frac{32\bigl(x-\tfrac\pi4\bigr)^5}{5!} + \ldots = \sum_{n=0}^\infty\frac{(-1)^{n-1}2^{2n+1}}{(2n+1)!} \bigl(x-\tfrac\pi4\bigr)^{2n+1}.
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