Find the limit of the sequence if it converges; otherwise indicate divergence. an = 7 + (0.9)", for n= 1, 2, 3, . O A. 7.9 В. 8 Ос. 7 O D. Diverges
Find the limit of the sequence if it converges; otherwise indicate divergence. an = 7 + (0.9)", for n= 1, 2, 3, . O A. 7.9 В. 8 Ос. 7 O D. Diverges
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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![**Exercise: Determine the Limit of the Sequence**
Consider the sequence defined by:
\[ a_n = 7 + (0.9)^n, \]
for \( n = 1, 2, 3, \ldots \)
Determine the limit of this sequence if it converges. If the sequence does not converge, indicate divergence.
**Options:**
- A. 7.9
- B. 8
- C. 7
- D. Diverges
**Explanation:**
The sequence \( a_n = 7 + (0.9)^n \) involves two parts: a constant term (7) and an exponential term \((0.9)^n\). As \( n \) increases, the exponential term \((0.9)^n\) approaches 0, because 0.9 is a number between 0 and 1.
Thus, the sequence \( a_n \) approaches the limit 7. Therefore, the correct answer is:
- C. 7](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F43abe65f-7e5f-4ca7-a91c-ab097f3acb86%2F84055761-1336-41d8-9345-3dc9c65b12dc%2Fh0tm5aa_processed.png&w=3840&q=75)
Transcribed Image Text:**Exercise: Determine the Limit of the Sequence**
Consider the sequence defined by:
\[ a_n = 7 + (0.9)^n, \]
for \( n = 1, 2, 3, \ldots \)
Determine the limit of this sequence if it converges. If the sequence does not converge, indicate divergence.
**Options:**
- A. 7.9
- B. 8
- C. 7
- D. Diverges
**Explanation:**
The sequence \( a_n = 7 + (0.9)^n \) involves two parts: a constant term (7) and an exponential term \((0.9)^n\). As \( n \) increases, the exponential term \((0.9)^n\) approaches 0, because 0.9 is a number between 0 and 1.
Thus, the sequence \( a_n \) approaches the limit 7. Therefore, the correct answer is:
- C. 7
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