6. State whether each telescoping series converges or diverges. If it converges, state the number that it converges to. i. ii. -1e-3n-e-3(n+1)
6. State whether each telescoping series converges or diverges. If it converges, state the number that it converges to. i. ii. -1e-3n-e-3(n+1)
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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![### Problem 6
**Objective:** State whether each telescoping series converges or diverges. If it converges, state the number that it converges to.
#### i.
\[ \sum_{n=1}^\infty \ln \left( \frac{n}{n+3} \right) \]
**Convergence:**
\[ \_\_\_\_\_\_\_\_\_\_\ ]
#### ii.
\[ \sum_{n=1}^\infty e^{-3n} - e^{-3(n+1)} \]
**Convergence:**
\[ \_\_\_\_\_\_\_\_\_\_\ ]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe8fabc15-e5db-480c-94d9-e42b67b656a8%2F4483d411-1ba0-41ff-8a2f-f0520b64b7e2%2Fbfsmiy_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem 6
**Objective:** State whether each telescoping series converges or diverges. If it converges, state the number that it converges to.
#### i.
\[ \sum_{n=1}^\infty \ln \left( \frac{n}{n+3} \right) \]
**Convergence:**
\[ \_\_\_\_\_\_\_\_\_\_\ ]
#### ii.
\[ \sum_{n=1}^\infty e^{-3n} - e^{-3(n+1)} \]
**Convergence:**
\[ \_\_\_\_\_\_\_\_\_\_\ ]
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