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(3n)" (2n + 50)" n=1

(3n)" (2n + 50)" 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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Determine whether it converges or diverges. Explain fully
The image shows a mathematical series: \[ \sum_{n=1}^{\infty} \frac{(3n)^n}{(2n + 50)^n} \] This expression represents an infinite sum, starting from \( n = 1 \) to infinity. The term inside the summation is the fraction \(\frac{(3n)^n}{(2n + 50)^n}\), where: - The numerator \((3n)^n\) indicates \(3n\) raised to the power of \(n\). - The denominator \((2n + 50)^n\) indicates \(2n + 50\) raised to the power of \(n\). This series can be analyzed for convergence or divergence, depending on how the terms behave as \( n \) approaches infinity.
Transcribed Image Text:The image shows a mathematical series: \[ \sum_{n=1}^{\infty} \frac{(3n)^n}{(2n + 50)^n} \] This expression represents an infinite sum, starting from \( n = 1 \) to infinity. The term inside the summation is the fraction \(\frac{(3n)^n}{(2n + 50)^n}\), where: - The numerator \((3n)^n\) indicates \(3n\) raised to the power of \(n\). - The denominator \((2n + 50)^n\) indicates \(2n + 50\) raised to the power of \(n\). This series can be analyzed for convergence or divergence, depending on how the terms behave as \( n \) approaches infinity.
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