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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Question
Determine if the following series diverges or converges,
and it converges, to what value?
![The image contains a mathematical expression as follows:
\[
\sum_{n=0}^{\infty} 3^{2+n} \cdot 2^{1-3n}
\]
This equation involves an infinite series beginning with \( n = 0 \) and summing to infinity. The term inside the summation consists of two exponential expressions:
- \( 3^{2+n} \) indicates that the base 3 is raised to the power of \( 2+n \).
- \( 2^{1-3n} \) indicates that the base 2 is raised to the power of \( 1-3n \).
The expression evaluates the combined influence of these exponential functions as \( n \) progresses from 0 to infinity.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faad9e4ed-ed50-4fe3-96ca-72ed3d364f6f%2F3ee7ef76-5f6b-430a-9f9c-9f7610fe98c1%2F6xre9hgm_processed.png&w=3840&q=75)
Transcribed Image Text:The image contains a mathematical expression as follows:
\[
\sum_{n=0}^{\infty} 3^{2+n} \cdot 2^{1-3n}
\]
This equation involves an infinite series beginning with \( n = 0 \) and summing to infinity. The term inside the summation consists of two exponential expressions:
- \( 3^{2+n} \) indicates that the base 3 is raised to the power of \( 2+n \).
- \( 2^{1-3n} \) indicates that the base 2 is raised to the power of \( 1-3n \).
The expression evaluates the combined influence of these exponential functions as \( n \) progresses from 0 to infinity.
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