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Power series

  1. Mar 28, 2006 #1
    Represent the function 5ln(7-x) as a power series, i.e., Maclaurin series,

    C_0=
    C_1=
    C_2=
    C_3=
    C_4=

    i got C_0 = 5 ln (7-0)

    and i think C_1 = 5/(7-1)

    but its wrong

    the textbook says that C_1 will be the derivative of C_0

    anyway.... please give me some hint
     
  2. jcsd
  3. Mar 28, 2006 #2

    Galileo

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    You forgot to apply the chain rule.
     
  4. Mar 28, 2006 #3
    okay thanx

    i got C_2 = -(5/7)

    but how come C_3 is not -5/49

    I think you just keep taking the derivative of the previous and set x = 0

    am I wrong?
     
  5. Mar 28, 2006 #4

    Galileo

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    Ehm, no, that's not the expression for the n-th coefficient of a Taylor series. (which should be in your book).

    But you can find out. If f function is written as:
    [tex]f(x)=\sum_{n=0}^\infty c_n (x-a)^n[/tex]
    what is [itex]c_n[/itex] in terms of f and/or its derivatives? (Assume you can interchange differentiation and summation).
     
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