n - 4 Sn The nth partial sum of the series 2n = 1 an is given by n + 5. Select the correct rule for a,or the actual nth term. Hint: an = Sn- Sn - 1 a 9. An (n + 5)(n + 3) b an (n + 5)(n + 4) -5 An (n + 3)(n + 2) 2n? +9 (n + 5)(n + 4) || || || ||
n - 4 Sn The nth partial sum of the series 2n = 1 an is given by n + 5. Select the correct rule for a,or the actual nth term. Hint: an = Sn- Sn - 1 a 9. An (n + 5)(n + 3) b an (n + 5)(n + 4) -5 An (n + 3)(n + 2) 2n? +9 (n + 5)(n + 4) || || || ||
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![The \( n^{th} \) partial sum of the series \( \sum_{n=1}^{\infty} a_n \) is given by \( S_n = \frac{n-4}{n+5} \).
Select the correct rule for \( a_n \), or the actual \( n^{th} \) term.
**Hint**: \( a_n = S_n - S_{n-1} \)
- **Option a:**
\[
a_n = \frac{9}{(n+5)(n+3)}
\]
- **Option b:**
\[
a_n = \frac{9}{(n+5)(n+4)}
\]
- **Option c:**
\[
a_n = \frac{-5}{(n+3)(n+2)}
\]
- **Option d:**
\[
a_n = \frac{2n^2 + 9}{(n+5)(n+4)}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe067374a-4fad-44f7-a999-a00988f990e9%2F745c582c-51fe-4142-9d3e-241809b99a7d%2Fg27hdmq_processed.png&w=3840&q=75)
Transcribed Image Text:The \( n^{th} \) partial sum of the series \( \sum_{n=1}^{\infty} a_n \) is given by \( S_n = \frac{n-4}{n+5} \).
Select the correct rule for \( a_n \), or the actual \( n^{th} \) term.
**Hint**: \( a_n = S_n - S_{n-1} \)
- **Option a:**
\[
a_n = \frac{9}{(n+5)(n+3)}
\]
- **Option b:**
\[
a_n = \frac{9}{(n+5)(n+4)}
\]
- **Option c:**
\[
a_n = \frac{-5}{(n+3)(n+2)}
\]
- **Option d:**
\[
a_n = \frac{2n^2 + 9}{(n+5)(n+4)}
\]
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