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2. Σ. 1 (-5) 2n n2gn

2. Σ. 1 (-5) 2n n2gn

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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Are the following series absolutely convergent, conditionally convergent, or divergent? (Use the appropriate test)
**Mathematical Expression:** This content is related to an infinite series, which is a sum of an infinite sequence of terms. Here's the transcription of the expression: 2. \(\sum_{n=1}^{\infty} \frac{(-5)^{2n}}{n^{2 9n}}\) **Explanation:** - **Notation:** The symbol \(\sum\) represents summation, which indicates that we are adding a sequence of terms. The limits of the sum, from \(n=1\) to \(\infty\), tell us that the sum starts at \(n=1\) and continues indefinitely (infinitely). - **Term Details:** - The term \((-5)^{2n}\) involves raising \(-5\) to the power of \(2n\). - The denominator \(n^{2 9n}\) involves raising \(n\) to the power of \(29n\). - **Overall Structure:** - The entire expression represents the sum of terms of the form \(\frac{(-5)^{2n}}{n^{29n}}\) for each integer value of \(n\) starting from 1 and going to infinity.
Transcribed Image Text:**Mathematical Expression:** This content is related to an infinite series, which is a sum of an infinite sequence of terms. Here's the transcription of the expression: 2. \(\sum_{n=1}^{\infty} \frac{(-5)^{2n}}{n^{2 9n}}\) **Explanation:** - **Notation:** The symbol \(\sum\) represents summation, which indicates that we are adding a sequence of terms. The limits of the sum, from \(n=1\) to \(\infty\), tell us that the sum starts at \(n=1\) and continues indefinitely (infinitely). - **Term Details:** - The term \((-5)^{2n}\) involves raising \(-5\) to the power of \(2n\). - The denominator \(n^{2 9n}\) involves raising \(n\) to the power of \(29n\). - **Overall Structure:** - The entire expression represents the sum of terms of the form \(\frac{(-5)^{2n}}{n^{29n}}\) for each integer value of \(n\) starting from 1 and going to infinity.
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