Find the interval of convergence for the given power series. 00 (x – 3)" п(-6)" n=1 The series is convergent from x = left end included (enter Y or N): to x = right end included (enter Y or N):
Find the interval of convergence for the given power series. 00 (x – 3)" п(-6)" n=1 The series is convergent from x = left end included (enter Y or N): to x = right end included (enter Y or N):
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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![#### Finding the Interval of Convergence
The power series given is:
\[ \sum_{n=1}^{\infty} \frac{(x-3)^n}{n(-6)^n} \]
To determine the interval of convergence for this power series, follow the steps below:
1. **Determine the radius of convergence (R):**
- Apply the Ratio Test or Root Test to determine the value of \(R\).
2. **Identify the interval of convergence:**
- Determine the open interval and then check the endpoints for convergence.
**Series Convergence:**
The series is convergent:
- From \( x = \) [Input the left endpoint value here], left end included (enter Y or N): [Input Y or N]
- To \( x = \) [Input the right endpoint value here], right end included (enter Y or N): [Input Y or N]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F80308a18-74a9-4811-ae0e-6f2ee2431daf%2F8347cdad-b401-489a-84c0-fa33a05d5353%2F32webg5.png&w=3840&q=75)
Transcribed Image Text:#### Finding the Interval of Convergence
The power series given is:
\[ \sum_{n=1}^{\infty} \frac{(x-3)^n}{n(-6)^n} \]
To determine the interval of convergence for this power series, follow the steps below:
1. **Determine the radius of convergence (R):**
- Apply the Ratio Test or Root Test to determine the value of \(R\).
2. **Identify the interval of convergence:**
- Determine the open interval and then check the endpoints for convergence.
**Series Convergence:**
The series is convergent:
- From \( x = \) [Input the left endpoint value here], left end included (enter Y or N): [Input Y or N]
- To \( x = \) [Input the right endpoint value here], right end included (enter Y or N): [Input Y or N]
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