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?
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) \(t_n = \frac{100}{n!}\)
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**(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?
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![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?](https://content.bartleby.com/qna-images/question/ff1b6656-acf4-4e95-902d-43b1d88f0837/39335088-9219-486e-a081-7babb0b92a0e/j1ccq1k_processed.jpeg)
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