QUESTION
Read Theorem 5.14 (Remainders in Alternating Series) in the textbook $\mathrm{e}^{\text {T }}$. The alternating series $\sum_{n=1}^{\infty}(-1)^{n} \frac{1}{3^{n} n}$ converges. (You do not need to prove this, but you can if you want to.) Suppose we approximate the sum of the series by the partial sum $S_{k}$. What is the smallest number $k$ could be if we want the error to be at most 0.001 ?
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