Use the appropriate error theorem to find the sequence bn in terms of N, such that +00 1 1 IE(-1)". < bN n3 + n2 + 1 | n3 + n2 + 1 n=1 n=1
Use the appropriate error theorem to find the sequence bn in terms of N, such that +00 1 1 IE(-1)". < bN n3 + n2 + 1 | n3 + n2 + 1 n=1 n=1
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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Hi, I need help with the question in the image.
![(i) Use the appropriate error theorem to find the sequence \( b_N \) in terms of \( N \), such that
\[
\left| \sum_{n=1}^{+\infty} (-1)^n \frac{1}{n^3 + n^2 + 1} - \sum_{n=1}^{N} (-1)^n \frac{1}{n^3 + n^2 + 1} \right| < b_N
\]
Justify your work.
(ii) Calculate the limit of the following series:
\[
\sum_{n=5}^{+\infty} \frac{8n^{+20} - 9n^{-4}}{10^n}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5111351b-1042-4886-8af2-a2d624148dd8%2F553b5c3e-6089-42be-9cdf-1e0d6921a0c8%2Fucf3ni_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(i) Use the appropriate error theorem to find the sequence \( b_N \) in terms of \( N \), such that
\[
\left| \sum_{n=1}^{+\infty} (-1)^n \frac{1}{n^3 + n^2 + 1} - \sum_{n=1}^{N} (-1)^n \frac{1}{n^3 + n^2 + 1} \right| < b_N
\]
Justify your work.
(ii) Calculate the limit of the following series:
\[
\sum_{n=5}^{+\infty} \frac{8n^{+20} - 9n^{-4}}{10^n}
\]
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