Show that the series ∞ 1 Σ n² +1 n=1 converges using the Integral Test. Don't forget to state whether the function f(x) you are using satisfies all required properties. Is there some other test you could have used? Explain briefly.
Show that the series ∞ 1 Σ n² +1 n=1 converges using the Integral Test. Don't forget to state whether the function f(x) you are using satisfies all required properties. Is there some other test you could have used? Explain briefly.
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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![**Problem 2.**
(a) Show that the series
\[
\sum_{{n=1}}^{\infty} \frac{1}{n^2 + 1}
\]
converges using the Integral Test. Don't forget to state whether the function \( f(x) \) you are using satisfies all required properties.
(b) Is there some other test you could have used? Explain briefly.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa1d5cb46-a845-43db-921b-209c3c017b1f%2F9cb533d2-1bd2-45c9-9157-20afaeb8ce4c%2F4kpwu1r_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 2.**
(a) Show that the series
\[
\sum_{{n=1}}^{\infty} \frac{1}{n^2 + 1}
\]
converges using the Integral Test. Don't forget to state whether the function \( f(x) \) you are using satisfies all required properties.
(b) Is there some other test you could have used? Explain briefly.
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