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The given problem shows a geometric series with the first term \( a = 9 \) and a common ratio \( r = -\frac{11}{9} \).

### Solution:
For a geometric series to converge, the absolute value of the common ratio must satisfy \( |r| < 1 \). Here, we have:
\[
|r| = \left| -\frac{11}{9} \right| = \frac{11}{9}
\]
Since \( \frac{11}{9} > 1 \), the series diverges.

### Answer:
1. **Does the series converge or diverge?**  
   - **Answer:** Diverges.

2. **Sum of the series:**
   - Since the series diverges, we should enter "DIVERGES" as the sum.

Would you like more details or have any questions?

### Related Questions:
1. How do we determine if a geometric series converges or diverges?
2. What is the formula for the sum of a convergent geometric series?
3. Why does a series with \( |r| > 1 \) diverge?
4. How can we find the sum of a finite geometric series even if it diverges?
5. What other types of series can converge even if some terms are greater than 1?

### Tip:
For a geometric series, always check the absolute value of the ratio \( |r| \) to decide if it converges or diverges.

Determine if the series 9 - 11 + 121/9 - 1331/81 + ... converges or diverges, and find the sum if it converges.

Learn how to determine if the series 9 - 11 + 121/9 - 1331/81 + ... converges or diverges. This problem covers key concepts in series and sequences, including the geometric series convergence theorem and the formula for sum of a geometric series. Suitable for college-level students studying calculus.

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