Consider the following power series. Let an = I = 2 lim n→∞ an R = n+1 = Find the interval I and radius of convergence R for the given power series. (Enter your answer for interval of convergence using interval notation.) n=1 6/1 x. Find the following limit. 9
Consider the following power series. Let an = I = 2 lim n→∞ an R = n+1 = Find the interval I and radius of convergence R for the given power series. (Enter your answer for interval of convergence using interval notation.) n=1 6/1 x. Find the following limit. 9
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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Question
![**Power Series Problem**
Consider the following power series:
\[
\sum_{n=1}^{\infty} \frac{9^n}{n} x^n
\]
Let \( a_n = \frac{9^n}{n} x^n \). Find the following limit:
\[
\lim_{n \to \infty} \left| \frac{a_{n+1}}{a_n} \right| = \_\_\_\_
\]
Find the interval \( I \) and radius of convergence \( R \) for the given power series. (Enter your answer for interval of convergence using interval notation.)
\[
I = \_\_\_\_
\]
\[
R = \frac{1}{9}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa103160f-6870-471c-8ca1-5357643d2f88%2F846791f6-c839-42df-a0da-12e2396a56ec%2Fk6paoxg_processed.png&w=3840&q=75)
Transcribed Image Text:**Power Series Problem**
Consider the following power series:
\[
\sum_{n=1}^{\infty} \frac{9^n}{n} x^n
\]
Let \( a_n = \frac{9^n}{n} x^n \). Find the following limit:
\[
\lim_{n \to \infty} \left| \frac{a_{n+1}}{a_n} \right| = \_\_\_\_
\]
Find the interval \( I \) and radius of convergence \( R \) for the given power series. (Enter your answer for interval of convergence using interval notation.)
\[
I = \_\_\_\_
\]
\[
R = \frac{1}{9}
\]
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