Lagrange remainder question.

  • Thread starter peripatein
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  • #1
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Hi,

Homework Statement


I am trying to limit Lagrange's remainder on taylor expansion of ln(4/5) to be ≤ 1/1000.


Homework Equations





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.
 

Answers and Replies

  • #2
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I am rather surprised no one has replied. Is there anything amiss with my formulation of the problem?
 
  • #3
haruspex
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Every time I keep getting that (n+1)4n+1≥1000, leading to n ≥ 3.
Please post your working to that point.
 

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