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Graph both the sequence of terms and the sequence of partial sums on the same screen. Use the graph to make a rough estimate of the sum of the series. Then use the Alternating Series Estimation Theorem to estimate the sum correct to four decimal places.

The series you provided is:

\[
\sum_{n=1}^{\infty} (-1)^{n-1} \frac{n}{6^n}
\]

### Steps:
1. **Graph the Sequence of Terms and Partial Sums:**
   - Plot the sequence of terms \( a_n = (-1)^{n-1} \frac{n}{6^n} \).
   - Plot the sequence of partial sums \( S_n = \sum_{k=1}^{n} (-1)^{k-1} \frac{k}{6^k} \).

2. **Estimate the Sum Using the Graph:**
   - Use the graph of the partial sums to make a rough estimate of the sum of the series as \( n \) increases.

3. **Use the Alternating Series Estimation Theorem:**
   - Apply the Alternating Series Estimation Theorem to estimate the sum to four decimal places.

Let's start by computing and graphing the sequences.

Learn how to graph the sequence of terms and partial sums of an alternating series and estimate its sum using the Alternating Series Estimation Theorem. Understand the application of series convergence techniques in advanced calculus.

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