### Problem Statement **3)** \[ \sum_{n=1}^{\infty} \frac{\cos n\pi}{\sqrt{n}} \] #### a) Write out \(\sum_{n=1}^{5} \frac{\cos n\pi}{\sqrt{n}}\) in expanded form, then simplify cosine values. #### b) State one possible test that can be applied to determine if the series is convergent or divergent. #### c) Show if the conditions for applying the test are met, then show all procedures applying the test for the given series. #### d) State the conclusion by what test that you applied. **Problem Statement:** 3) (c) Show if the series is conditionally convergent, absolutely convergent, or divergent.
### Problem Statement **3)** \[ \sum_{n=1}^{\infty} \frac{\cos n\pi}{\sqrt{n}} \] #### a) Write out \(\sum_{n=1}^{5} \frac{\cos n\pi}{\sqrt{n}}\) in expanded form, then simplify cosine values. #### b) State one possible test that can be applied to determine if the series is convergent or divergent. #### c) Show if the conditions for applying the test are met, then show all procedures applying the test for the given series. #### d) State the conclusion by what test that you applied. **Problem Statement:** 3) (c) Show if the series is conditionally convergent, absolutely convergent, or divergent.
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
![### Problem Statement
**3)**
\[
\sum_{n=1}^{\infty} \frac{\cos n\pi}{\sqrt{n}}
\]
#### a)
Write out \(\sum_{n=1}^{5} \frac{\cos n\pi}{\sqrt{n}}\) in expanded form, then simplify cosine values.
#### b)
State one possible test that can be applied to determine if the series is convergent or divergent.
#### c)
Show if the conditions for applying the test are met, then show all procedures applying the test for the given series.
#### d)
State the conclusion by what test that you applied.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56f2bffd-1d3a-4b76-92a6-52fd8f44fbf4%2Fee74c697-90ff-4514-b5cc-d86d0e324b1c%2Ffiosxad.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
**3)**
\[
\sum_{n=1}^{\infty} \frac{\cos n\pi}{\sqrt{n}}
\]
#### a)
Write out \(\sum_{n=1}^{5} \frac{\cos n\pi}{\sqrt{n}}\) in expanded form, then simplify cosine values.
#### b)
State one possible test that can be applied to determine if the series is convergent or divergent.
#### c)
Show if the conditions for applying the test are met, then show all procedures applying the test for the given series.
#### d)
State the conclusion by what test that you applied.
Transcribed Image Text:**Problem Statement:**
3) (c) Show if the series is conditionally convergent, absolutely convergent, or divergent.
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