Practice: Show that if C71, then the series is convergent. EMIAN² NCIn
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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![Practice: Show that if \( c > 1 \), then the series is convergent.
\[
\sum \frac{1}{N(\ln N)^c}
\]
This exercise involves proving the convergence of a mathematical series. The series in question is represented by the summation symbol \(\sum\) and consists of terms of the form \(\frac{1}{N(\ln N)^c}\), where \(N\) is a variable and \(c\) is a constant greater than 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe57a7d70-87de-4a1f-8104-5b2578062c6c%2F0cc727b7-86ca-48b5-8baa-7766f14655b8%2Fqhb0mtq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Practice: Show that if \( c > 1 \), then the series is convergent.
\[
\sum \frac{1}{N(\ln N)^c}
\]
This exercise involves proving the convergence of a mathematical series. The series in question is represented by the summation symbol \(\sum\) and consists of terms of the form \(\frac{1}{N(\ln N)^c}\), where \(N\) is a variable and \(c\) is a constant greater than 1.
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Step 1: Proof for c=1
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