Compute the value of the following improper integral. If it converges, enter its value. Enter infinity if it diverges to ∞, and -infinity if it diverges to -∞. Otherwise, enter diverges. S 2 dx x² +1 = Does the series ∞ n=1 2 n² + 1 converge or diverge? ?
Compute the value of the following improper integral. If it converges, enter its value. Enter infinity if it diverges to ∞, and -infinity if it diverges to -∞. Otherwise, enter diverges. S 2 dx x² +1 = Does the series ∞ n=1 2 n² + 1 converge or diverge? ?
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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![Compute the value of the following improper integral. If it converges, enter its value. Enter **infinity** if it diverges to ∞, and **-infinity** if it diverges to -∞. Otherwise, enter **diverges**.
\[
\int_{1}^{\infty} \frac{2 \, dx}{x^2 + 1} = \, \square
\]
Does the series
\[
\sum_{n=1}^{\infty} \frac{2}{n^2 + 1}
\]
converge or diverge? [Dropdown menu]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdd3494d7-16cb-4f96-a1a3-f69334a1e65b%2F989a849f-0c18-4c1c-b5f2-3210cd6995a4%2Fq55cke_processed.png&w=3840&q=75)
Transcribed Image Text:Compute the value of the following improper integral. If it converges, enter its value. Enter **infinity** if it diverges to ∞, and **-infinity** if it diverges to -∞. Otherwise, enter **diverges**.
\[
\int_{1}^{\infty} \frac{2 \, dx}{x^2 + 1} = \, \square
\]
Does the series
\[
\sum_{n=1}^{\infty} \frac{2}{n^2 + 1}
\]
converge or diverge? [Dropdown menu]
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