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M8 n=1 4 (4n – 3)(4n + 1)

M8 n=1 4 (4n – 3)(4n + 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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Find the sum of the series.
\[ \sum_{n=1}^{\infty} \frac{4}{(4n - 3)(4n + 1)} \] This formula represents an infinite series starting from \( n = 1 \) to infinity. The general term of the series is given by \( \frac{4}{(4n - 3)(4n + 1)} \). Here, the numerator is a constant 4, and the denominator is the product of two linear expressions in \( n \), specifically \( (4n - 3) \) and \( (4n + 1) \). Understanding this series might involve evaluating convergence or applying specific summation techniques.
Transcribed Image Text:\[ \sum_{n=1}^{\infty} \frac{4}{(4n - 3)(4n + 1)} \] This formula represents an infinite series starting from \( n = 1 \) to infinity. The general term of the series is given by \( \frac{4}{(4n - 3)(4n + 1)} \). Here, the numerator is a constant 4, and the denominator is the product of two linear expressions in \( n \), specifically \( (4n - 3) \) and \( (4n + 1) \). Understanding this series might involve evaluating convergence or applying specific summation techniques.
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