Determine whether the series converges. (5) k=1 3k+2 2k-1 k
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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![**Determine whether the series converges:**
1. **Series (5):**
\[
\sum_{k=1}^{\infty} \left( \frac{3k+2}{2k-1} \right)^k
\]
2. **Series (6):**
\[
\sum_{k=1}^{\infty} k^{50} e^{-k}
\]
3. **Series (7):**
\[
\sum_{k=1}^{\infty} \frac{\ln k}{e^k}
\]
Each series is expressed using summation notation from \( k = 1 \) to infinity. The task is to assess whether each infinite series converges or diverges.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc57f7e0d-797b-4b4c-aff5-3e2cb2f516c9%2Fcbcf7b26-b25c-4e9f-aa31-ae7628ef4fb4%2F6dqojip_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Determine whether the series converges:**
1. **Series (5):**
\[
\sum_{k=1}^{\infty} \left( \frac{3k+2}{2k-1} \right)^k
\]
2. **Series (6):**
\[
\sum_{k=1}^{\infty} k^{50} e^{-k}
\]
3. **Series (7):**
\[
\sum_{k=1}^{\infty} \frac{\ln k}{e^k}
\]
Each series is expressed using summation notation from \( k = 1 \) to infinity. The task is to assess whether each infinite series converges or diverges.
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