(3k³ + 4)(7k² + 1) (2k³ + 1)(4k³ – 1) 21. E k=1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Using the Direct Comparison Test or the Limit Comparison Test determine if the series converges or diverges.
![The image displays a mathematical expression for a series, which is part of a problem labeled as "21". The expression within the series is:
\[
\sum_{{k=1}}^{\infty} \frac{(3k^3 + 4)(7k^2 + 1)}{(2k^3 + 1)(4k^3 - 1)}
\]
This series summation runs from \( k = 1 \) to infinity. The expression inside the summation is a rational function, where:
- The numerator is \((3k^3 + 4)(7k^2 + 1)\).
- The denominator is \((2k^3 + 1)(4k^3 - 1)\).
This problem would typically be used in a calculus or advanced mathematics course exploring infinite series or sequences.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9a36eedc-1311-4ac7-908a-8a22bc0a900c%2F409deaaa-3d13-44ea-9beb-daf771dd6e5d%2Flu1oelx_processed.png&w=3840&q=75)
Transcribed Image Text:The image displays a mathematical expression for a series, which is part of a problem labeled as "21". The expression within the series is:
\[
\sum_{{k=1}}^{\infty} \frac{(3k^3 + 4)(7k^2 + 1)}{(2k^3 + 1)(4k^3 - 1)}
\]
This series summation runs from \( k = 1 \) to infinity. The expression inside the summation is a rational function, where:
- The numerator is \((3k^3 + 4)(7k^2 + 1)\).
- The denominator is \((2k^3 + 1)(4k^3 - 1)\).
This problem would typically be used in a calculus or advanced mathematics course exploring infinite series or sequences.
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