See attachment
Is there a better way to do this problem?
For the following convergent series, at least how many terms do you have to sum so that the partial sum is within 0.001 of the sum of the series?
If you add the first k terms, the remainder is
Using the fact that
take the derivative of both sides
let x=1
so we want
but that can't be solved explicitly for k
although it appears to be true for k >8
If interested I have the proof of this Theorem on my web site
Infinie Series