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## 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 x

_{0}(the center)=0, and ln(x), where x=4/5 and x

_{0}=1.

Every time I keep getting that (n+1)4

^{n+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.