12a) n=l 3+1 22n-3 12b) M=1 1 'n' + 9n + 20
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
Find the limits of these series. Please show and label each step.
![### Infinite Series Problems
#### Problem 12a:
Evaluate the infinite series:
\[
\sum_{n=1}^{\infty} \frac{3^{n+1}}{2^{2n-3}}
\]
#### Problem 12b:
Evaluate the infinite series:
\[
\sum_{n=1}^{\infty} \frac{1}{n^2 + 9n + 20}
\]
These problems involve the evaluation of infinite series. For problem 12a, the series is given in terms of a ratio involving exponential expressions. For problem 12b, the series involves a quadratic polynomial in the denominator.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5456dffd-fe15-479d-aec2-2e26d1f45f3e%2F292a8a22-f376-425f-838b-a3529ca0397e%2Fcz7h25_processed.png&w=3840&q=75)
Transcribed Image Text:### Infinite Series Problems
#### Problem 12a:
Evaluate the infinite series:
\[
\sum_{n=1}^{\infty} \frac{3^{n+1}}{2^{2n-3}}
\]
#### Problem 12b:
Evaluate the infinite series:
\[
\sum_{n=1}^{\infty} \frac{1}{n^2 + 9n + 20}
\]
These problems involve the evaluation of infinite series. For problem 12a, the series is given in terms of a ratio involving exponential expressions. For problem 12b, the series involves a quadratic polynomial in the denominator.
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