Find the sum of the convergent series. (Round your answer to four decimal places.) Σ (sin(1))" n = 1 0.0178 X
Find the sum of the convergent series. (Round your answer to four decimal places.) Σ (sin(1))" n = 1 0.0178 X
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Problem Statement:**
Find the sum of the convergent series. (Round your answer to four decimal places.)
\[ \sum_{n=1}^{\infty} (\sin(1))^n \]
**Answer:**
0.0178
**Explanation:**
This series is an infinite geometric series where each term is of the form \((\sin(1))^n\). In a geometric series with first term \(a\) and common ratio \(r\), the sum \(S\) of the infinite series is given by:
\[ S = \frac{a}{1 - r} \]
where \(0 < |r| < 1\).
Here, the first term \(a = \sin(1)\) and the common ratio \(r = \sin(1)\). The sum is calculated and rounded to four decimal places. The answer provided is 0.0178, indicating the sum of this convergent series.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F07f64844-f44f-4fd0-96ac-4d29f63737de%2F0cba7df1-0b0b-4571-9e49-91746fd25e1f%2F239xjbc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the sum of the convergent series. (Round your answer to four decimal places.)
\[ \sum_{n=1}^{\infty} (\sin(1))^n \]
**Answer:**
0.0178
**Explanation:**
This series is an infinite geometric series where each term is of the form \((\sin(1))^n\). In a geometric series with first term \(a\) and common ratio \(r\), the sum \(S\) of the infinite series is given by:
\[ S = \frac{a}{1 - r} \]
where \(0 < |r| < 1\).
Here, the first term \(a = \sin(1)\) and the common ratio \(r = \sin(1)\). The sum is calculated and rounded to four decimal places. The answer provided is 0.0178, indicating the sum of this convergent series.
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