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Maclaurin Polynomials

  1. Jul 24, 2012 #1
    1. Find the Maclaurin polynomials of order n = 0, 1, 2, 3, and 4, and then find the nth MacLaurin polynomials for the function in sigma notation.

    cos(∏x)





    2. Here is what I did:
    p0x = cos (0∏) = 1
    p1x = cos(0∏) - ∏sin(0∏)x = 1
    p2x = cos(0∏) - ∏sin(0∏)x -[itex]\frac{∏2(cos∏x)(x2)}{2!}[/itex](

    and so on.....

    And the pattern that forms are that the odd values for k are 0.

    So p0x = p1x
    and p2x = p3x

    etc etc.

    fk(x) = (∏)kcos(∏x)'
    and fk(0) = (∏)k(-1)k

    As for the sigma notation:

    Here is what I obtained:
    Ʃnk = 0([itex]\frac{(∏2k(-1)k}{k!}[/itex](x)2k

    According to the solution manual however, there is a n/2 on top of the sigma notation instead of a n.

    I don't understand .
     
  2. jcsd
  3. Jul 24, 2012 #2

    LCKurtz

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    Gold Member

    No. That isn't right if k is odd.

    I think the only thing wrong with your final answer is you should have a ##(2k)!## in the denominator. Then note that your general sum gives only the even powers, which are the only non-zero terms. Your book's answer probably has something to do with indexing it differently. Hard to say without seeing it.
     
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