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Lagrange remainder question.

  1. Dec 26, 2012 #1
    1. The problem statement, all variables and given/known data
    I am trying to limit Lagrange's remainder on taylor expansion of ln(4/5) to be ≤ 1/1000.

    2. Relevant equations

    3. The attempt at a solution
    I have tried using both ln(1+x), where x=-1/5 and x0(the center)=0, and ln(x), where x=4/5 and x0=1.
    Every time I keep getting that (n+1)4n+1≥1000, leading to n ≥ 3.
    But then, upon expansion up to the third power, I keep getting a result whose error is greater than the desired 1/1000. It appears the result should have been n≥4, but why so when algebra seems to prove it not to be the case?
    I'd appreciate some advice. Obviously I am missing something.
  2. jcsd
  3. Dec 26, 2012 #2
    I am rather surprised no one has replied. Is there anything amiss with my formulation of the problem?
  4. Dec 26, 2012 #3


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    Please post your working to that point.
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