Find the values of x for which the series converges. (Enter your answer using interval notation.) E (x + 4)" n = 1
Find the values of x for which the series converges. (Enter your answer using interval notation.) E (x + 4)" n = 1
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 values of \( x \) for which the series converges. (Enter your answer using interval notation.)
\[
\sum_{n=1}^{\infty} (x + 4)^n
\]
**Instructions:**
- Determine the interval of convergence for the given series.
- Enter your answer in interval notation in the provided box.
**Explanation:**
This is an infinite geometric series. For the series to converge, the common ratio \((x + 4)\) must satisfy:
\[
|x + 4| < 1
\]
Solve this inequality to find the values of \( x \) that ensure convergence.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe040b111-4b10-4c24-8337-c45ed461242d%2F93a11b53-8960-49dc-bfe8-d59ce214f163%2F419lnwm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the values of \( x \) for which the series converges. (Enter your answer using interval notation.)
\[
\sum_{n=1}^{\infty} (x + 4)^n
\]
**Instructions:**
- Determine the interval of convergence for the given series.
- Enter your answer in interval notation in the provided box.
**Explanation:**
This is an infinite geometric series. For the series to converge, the common ratio \((x + 4)\) must satisfy:
\[
|x + 4| < 1
\]
Solve this inequality to find the values of \( x \) that ensure convergence.
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