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Σ n=1 4n2 + 6 8n1 + n + 1

Σ n=1 4n2 + 6 8n1 + n + 1

Calculus: Early Transcendentals
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.
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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