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
![**Select the Convergent Series**
- **Option A:**
\[
\sum_{{n=1}}^{\infty} n^{16} \arctan\left(\frac{1}{n^{11}}\right)
\]
- **Option B:**
\[
\sum_{{n=1}}^{\infty} \sin\left(\frac{\pi}{2n+1}\right)
\]
- **Option C:**
\[
\sum_{{n=1}}^{\infty} n \tan\left(\frac{\pi}{2n+1}\right)
\]
- **Option D:**
\[
\sum_{{n=1}}^{\infty} n \ln\left(1+\frac{\pi}{2n+1}\right)
\]
- **Option E:**
\[
\sum_{{n=1}}^{\infty} 5^n \ln\left(1+\frac{5}{2n+1}\right)
\]
- **Option F:**
\[
\sum_{{n=1}}^{\infty} n^{16} \sin\left(\frac{2^n}{5^n}\right)
\]
**Diagrams or Graphs:**
There are no diagrams or graphs included in this image. If any graphs were present, a detailed analysis and description would be provided here.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F20554f75-6ffa-4470-9c61-2b37bb946b23%2Fc901d3e1-4538-43d7-8039-a6db95c13c75%2Fhf4s3m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Select the Convergent Series**
- **Option A:**
\[
\sum_{{n=1}}^{\infty} n^{16} \arctan\left(\frac{1}{n^{11}}\right)
\]
- **Option B:**
\[
\sum_{{n=1}}^{\infty} \sin\left(\frac{\pi}{2n+1}\right)
\]
- **Option C:**
\[
\sum_{{n=1}}^{\infty} n \tan\left(\frac{\pi}{2n+1}\right)
\]
- **Option D:**
\[
\sum_{{n=1}}^{\infty} n \ln\left(1+\frac{\pi}{2n+1}\right)
\]
- **Option E:**
\[
\sum_{{n=1}}^{\infty} 5^n \ln\left(1+\frac{5}{2n+1}\right)
\]
- **Option F:**
\[
\sum_{{n=1}}^{\infty} n^{16} \sin\left(\frac{2^n}{5^n}\right)
\]
**Diagrams or Graphs:**
There are no diagrams or graphs included in this image. If any graphs were present, a detailed analysis and description would be provided here.
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