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Taylor Series

  1. Mar 25, 2004 #1
    Find the 4th term of the Taylor series centerd at x=1 for f(x)=ln(x+1)

    f(x)=ln(1=x)
    f'(x)=(1+x)^-1
    f"(x)=(-1)[(1+x)^-2]
    f"'(x)=(2)[(1+x)^-3]
    f""(x)=-6[(1+x)^-4)]

    Plug in 1:
    .6931
    .5
    -.25
    .25
    -.375

    What do I do next? (Also, is the 4th term the 4th term starting with f(x)? or the 4th derivative?)
     
  2. jcsd
  3. Mar 25, 2004 #2
    it would be easier to start with the series for 1/(1+x) which is close to the geometric series. then integrate that to get the series for ln(1+x). then just look at the correct coefficient.
     
  4. Mar 26, 2004 #3

    matt grime

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    Science Advisor
    Homework Helper

    Don't use decimals, please, your teacher should be happier that way. And the 4'th (non-zero) term is exactly that, write down the taylor series, and pick out the 4th term in it (the x^3 term here).
     
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