A sequence is a list of numbers written in a definite order: Each number is called a ..., an a1, A2, A3, A4, called the a) an = For each of the following sequences, tell whether they converge or diverge as n → ∞o n b) bn = 1 - 2n 2n c) bn 3n+4 (11.2) The successor to an is represented by A sequence can be considered a function whose domain is d) an = sin n (-1)" 3+5 100 n! and an is e) an = f) tn A series is the sum of the terms of a sequence. To indicate the sum, we use sigma E notation. Write the following infinite sum in 2 notation: 1+3+9+27+81 +... What is the formula for the sum of an infinite geometric series? Under what conditions is this sum finite?
A sequence is a list of numbers written in a definite order: Each number is called a ..., an a1, A2, A3, A4, called the a) an = For each of the following sequences, tell whether they converge or diverge as n → ∞o n b) bn = 1 - 2n 2n c) bn 3n+4 (11.2) The successor to an is represented by A sequence can be considered a function whose domain is d) an = sin n (-1)" 3+5 100 n! and an is e) an = f) tn A series is the sum of the terms of a sequence. To indicate the sum, we use sigma E notation. Write the following infinite sum in 2 notation: 1+3+9+27+81 +... What is the formula for the sum of an infinite geometric series? Under what conditions is this sum finite?
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...
Related questions
Question
![A sequence is a list of numbers written in a definite order:
\(a_1, a_2, a_3, a_4, \ldots, a_n, \ldots\). Each number is called a **term**, and \(a_n\) is called the **nth term**. The successor to \(a_n\) is represented by \(a_{n+1}\). A sequence can be considered a function whose domain is the **positive integers**.
For each of the following sequences, tell whether they converge or diverge as \(n \to \infty\).
a) \(a_n = \frac{1}{n}\)
b) \(b_n = 1 - 2n\)
c) \(b_n = \frac{2n}{3n+4}\)
d) \(a_n = \sin n\)
e) \(a_n = \frac{(-1)^n}{3^n + 5}\)
f) \(t_n = \frac{100}{n!}\)
---
**(11.2)**
A series is the sum of the terms of a sequence. To indicate the sum, we use sigma \(\Sigma\) notation. Write the following infinite sum in \(\Sigma\) notation:
\[1 + 3 + 9 + 27 + 81 + \ldots\]
What is the formula for the sum of an infinite geometric series?
Under what conditions is this sum finite?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fff1b6656-acf4-4e95-902d-43b1d88f0837%2F39335088-9219-486e-a081-7babb0b92a0e%2Fj1ccq1k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A sequence is a list of numbers written in a definite order:
\(a_1, a_2, a_3, a_4, \ldots, a_n, \ldots\). Each number is called a **term**, and \(a_n\) is called the **nth term**. The successor to \(a_n\) is represented by \(a_{n+1}\). A sequence can be considered a function whose domain is the **positive integers**.
For each of the following sequences, tell whether they converge or diverge as \(n \to \infty\).
a) \(a_n = \frac{1}{n}\)
b) \(b_n = 1 - 2n\)
c) \(b_n = \frac{2n}{3n+4}\)
d) \(a_n = \sin n\)
e) \(a_n = \frac{(-1)^n}{3^n + 5}\)
f) \(t_n = \frac{100}{n!}\)
---
**(11.2)**
A series is the sum of the terms of a sequence. To indicate the sum, we use sigma \(\Sigma\) notation. Write the following infinite sum in \(\Sigma\) notation:
\[1 + 3 + 9 + 27 + 81 + \ldots\]
What is the formula for the sum of an infinite geometric series?
Under what conditions is this sum finite?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning