Determine whether the series is convergent or divergent by expressing s, as a telescoping sum (a 15 n(n + 3) n = 1 convergent divergent If it is convergent, find its sum. (If the quantity diverges, enter DIVERGES.) 11 6
Determine whether the series is convergent or divergent by expressing s, as a telescoping sum (a 15 n(n + 3) n = 1 convergent divergent If it is convergent, find its sum. (If the quantity diverges, enter DIVERGES.) 11 6
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![**Problem Statement:**
Determine whether the series is convergent or divergent by expressing \( s_n \) as a telescoping sum (as in Example 8).
\[ \sum_{n=1}^{\infty} \frac{15}{n(n+3)} \]
**Solution Options:**
- [x] Convergent
- [ ] Divergent
**Next Steps:**
If it is convergent, find its sum. (If the quantity diverges, enter DIVERGES.)
Entered Answer: \(\frac{11}{6}\) ❌
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**Explanation:**
In this problem, the series is identified as convergent, represented by the checked box under the "convergent" option. However, the attempt to find the sum, \(\frac{11}{6}\), is incorrect. The task involves expressing the series using a telescoping sum, which simplifies the process of determining convergence and finding the correct sum if it exists.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F805df41e-b889-4c16-a267-318b4eb3cf21%2F93523802-44ed-4489-817d-255cf8410b0e%2F946pdts_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Determine whether the series is convergent or divergent by expressing \( s_n \) as a telescoping sum (as in Example 8).
\[ \sum_{n=1}^{\infty} \frac{15}{n(n+3)} \]
**Solution Options:**
- [x] Convergent
- [ ] Divergent
**Next Steps:**
If it is convergent, find its sum. (If the quantity diverges, enter DIVERGES.)
Entered Answer: \(\frac{11}{6}\) ❌
---
**Explanation:**
In this problem, the series is identified as convergent, represented by the checked box under the "convergent" option. However, the attempt to find the sum, \(\frac{11}{6}\), is incorrect. The task involves expressing the series using a telescoping sum, which simplifies the process of determining convergence and finding the correct sum if it exists.
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