2) Which of the following series converge absolutely, which converge, and which diverge? Give reasons for your answers. Inn a) Ex-1(-1)" (1-1) n=1 b) 1 + 1/2 1 9 T 1 1 + 16 25 +36-1/29 - 12/+--- 49 64
2) Which of the following series converge absolutely, which converge, and which diverge? Give reasons for your answers. Inn a) Ex-1(-1)" (1-1) n=1 b) 1 + 1/2 1 9 T 1 1 + 16 25 +36-1/29 - 12/+--- 49 64
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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quick pls and explain the problem with step by step
![**Question 2: Analysis of Series Convergence**
Determine which of the following series converge absolutely, which converge, and which diverge. Provide reasons for your answers.
**a) Series:**
\[
\sum_{n=1}^{\infty} (-1)^n \left( \frac{\ln n}{n - \ln n} \right)
\]
**b) Series:**
\[
1 + \frac{1}{4} - \frac{1}{9} + \frac{1}{16} + \frac{1}{25} - \frac{1}{36} + \frac{1}{49} - \frac{1}{64} + \ldots
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8d2af6b8-35d3-4327-94c1-a05ff77beaf0%2F5b24be92-04dc-41bc-879a-895957b55314%2Fv9ad7kb_processed.png&w=3840&q=75)
Transcribed Image Text:**Question 2: Analysis of Series Convergence**
Determine which of the following series converge absolutely, which converge, and which diverge. Provide reasons for your answers.
**a) Series:**
\[
\sum_{n=1}^{\infty} (-1)^n \left( \frac{\ln n}{n - \ln n} \right)
\]
**b) Series:**
\[
1 + \frac{1}{4} - \frac{1}{9} + \frac{1}{16} + \frac{1}{25} - \frac{1}{36} + \frac{1}{49} - \frac{1}{64} + \ldots
\]
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