Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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show that the series converges or diveregs
![This mathematical expression represents an infinite series. The general form of the term in the series is:
\[ \sum_{n=1}^{\infty} \frac{4n^2 + 6}{8n^7 + n + 1} \]
This notation can be read as:
"The sum from \( n = 1 \) to infinity of the fraction \(\frac{4n^2 + 6}{8n^7 + n + 1}\)."
Explanation:
- \(\sum\) denotes the summation symbol, indicating that you're summing up a series of terms.
- The limits of the summation are \( n = 1 \) at the lower end and extending to infinity at the upper end.
- Each term in the series is defined by the fraction \(\frac{4n^2 + 6}{8n^7 + n + 1}\).
This series is typically analyzed to determine its convergence or divergence by various methods in calculus.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff24651e9-0a43-4fcf-8170-c5e34dc6dcab%2Fe7d9e6d7-2f9f-449e-8b75-304d50338134%2Fnkogw8_processed.png&w=3840&q=75)
Transcribed Image Text:This mathematical expression represents an infinite series. The general form of the term in the series is:
\[ \sum_{n=1}^{\infty} \frac{4n^2 + 6}{8n^7 + n + 1} \]
This notation can be read as:
"The sum from \( n = 1 \) to infinity of the fraction \(\frac{4n^2 + 6}{8n^7 + n + 1}\)."
Explanation:
- \(\sum\) denotes the summation symbol, indicating that you're summing up a series of terms.
- The limits of the summation are \( n = 1 \) at the lower end and extending to infinity at the upper end.
- Each term in the series is defined by the fraction \(\frac{4n^2 + 6}{8n^7 + n + 1}\).
This series is typically analyzed to determine its convergence or divergence by various methods in calculus.
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