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
Using the given formula for Sn I need help figuring out which of the four choices below is correct and why the others are incorrect.
Transcribed Image Text:(a.) \(\sum a_n\) converges and \(\{s_n\}\) converges.
(b.) \(\sum a_n\) converges and \(\{s_n\}\) diverges.
(c.) \(\sum a_n\) diverges and \(\{s_n\}\) converges.
(d.) \(\sum a_n\) diverges and \(\{s_n\}\) diverges.
![The image shows a mathematical expression for \( s_n \) which is defined as:
\[
s_n = \frac{3n + 1}{4n - n}
\]
This is a formula that likely represents a sequence or a series in mathematics, where \( n \) is a variable. The formula is composed of a fraction, where the numerator is \( 3n + 1 \) and the denominator simplifies to \( 3n \) (since \( 4n - n = 3n \)). Therefore, the simplified form of the expression is \( s_n = 1 + \frac{1}{3n} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb4f8469-eda0-4bfd-b67e-0d596825d7c6%2Fcf2a7eff-4be7-4543-beae-c92c879709d2%2F87z7poi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image shows a mathematical expression for \( s_n \) which is defined as:
\[
s_n = \frac{3n + 1}{4n - n}
\]
This is a formula that likely represents a sequence or a series in mathematics, where \( n \) is a variable. The formula is composed of a fraction, where the numerator is \( 3n + 1 \) and the denominator simplifies to \( 3n \) (since \( 4n - n = 3n \)). Therefore, the simplified form of the expression is \( s_n = 1 + \frac{1}{3n} \).
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