Hi, 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.