1 Use the integral test to determine whether > converges. n2 + 1 n=0 A. the series diverges B. the series converges to a number more than C. the series converges to D. the series converges to a number less than 2
1 Use the integral test to determine whether > converges. n2 + 1 n=0 A. the series diverges B. the series converges to a number more than C. the series converges to D. the series converges to a number less than 2
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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![**Using the Integral Test to Determine Series Convergence**
Evaluate the convergence of the series given by:
\[
\sum_{n=0}^{\infty} \frac{1}{n^2 + 1}
\]
Select the appropriate conclusion about the series:
- **A.** The series diverges.
- **B.** The series converges to a number more than \(\frac{\pi}{2}\).
- **C.** The series converges to \(\frac{\pi}{2}\).
- **D.** The series converges to a number less than \(\frac{\pi}{2}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac325f2c-c68e-4255-b157-3d6a2ed23174%2F48ccb490-4468-43f3-b76f-84e3f08e2c47%2Fobico0f_processed.png&w=3840&q=75)
Transcribed Image Text:**Using the Integral Test to Determine Series Convergence**
Evaluate the convergence of the series given by:
\[
\sum_{n=0}^{\infty} \frac{1}{n^2 + 1}
\]
Select the appropriate conclusion about the series:
- **A.** The series diverges.
- **B.** The series converges to a number more than \(\frac{\pi}{2}\).
- **C.** The series converges to \(\frac{\pi}{2}\).
- **D.** The series converges to a number less than \(\frac{\pi}{2}\).
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