Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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: \[ \sum_{n=5}^{+\infty} \frac{8n^{+20} - 9n^{-4}}{10^n} \]
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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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