Define 1 1 + (−1)n-1 an = 1 - ln 2. 2 3 n Show that 1 an converges and determine its sum. n=1 +
Define 1 1 + (−1)n-1 an = 1 - ln 2. 2 3 n Show that 1 an converges and determine its sum. 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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![Define
\[ a_n = 1 - \frac{1}{2} + \frac{1}{3} - \cdots + \frac{(-1)^{n-1}}{n} - \ln 2. \]
Show that \( \sum_{n=1}^{\infty} a_n \) converges and determine its sum.
Use the given series (and all pertinent theorems and techniques) to perform this evaluation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1d5e88e6-b1af-4aea-9b08-2dadd85f5e2c%2F7213a9dc-6953-4670-ac9d-fbb16e3fa8ed%2Ft78xxq_processed.png&w=3840&q=75)
Transcribed Image Text:Define
\[ a_n = 1 - \frac{1}{2} + \frac{1}{3} - \cdots + \frac{(-1)^{n-1}}{n} - \ln 2. \]
Show that \( \sum_{n=1}^{\infty} a_n \) converges and determine its sum.
Use the given series (and all pertinent theorems and techniques) to perform this evaluation.
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