Question
True or False If the alternating series $\sum_{k=1}^{\infty}(-1)^{k+1} a_{k}$ satisfies the two conditions of the Alternating Series Test, then the error $E_{n}$ in using the sum $S_{n}$ of the first $n$ terms as an approximation of the $\operatorname{sum} S$ of the series is $\left|E_{n}\right| \leq a_{n}$
Step 1
A series $\sum_{k=1}^{\infty}(-1)^{k+1} a_{k}$ converges if: - $a_{k+1} \leq a_{k}$ for all $k$, i.e., the terms $a_{k}$ are decreasing, and - $\lim_{k \to \infty} a_{k} = 0$. Show more…
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