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Problem 5. the Ratio Test. (a) 8 n=1 πn n! State whether each of the following series converges or diverges using (0) Σ n=1 n! πn

Problem 5. the Ratio Test. (a) 8 n=1 πn n! State whether each of the following series converges or diverges using (0) Σ n=1 n! πn

Advanced Engineering Mathematics
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 5.** State whether each of the following series converges or diverges using the Ratio Test. (a) \( \sum_{n=1}^{\infty} \frac{\pi^n}{n!} \) (b) \( \sum_{n=1}^{\infty} \frac{n!}{\pi^n} \) - In this problem, two infinite series are presented. The task is to determine if each series converges or diverges by applying the Ratio Test. - The Ratio Test involves analyzing the limit of the absolute value of the ratio of consecutive terms in the series.
Transcribed Image Text:**Problem 5.** State whether each of the following series converges or diverges using the Ratio Test. (a) \( \sum_{n=1}^{\infty} \frac{\pi^n}{n!} \) (b) \( \sum_{n=1}^{\infty} \frac{n!}{\pi^n} \) - In this problem, two infinite series are presented. The task is to determine if each series converges or diverges by applying the Ratio Test. - The Ratio Test involves analyzing the limit of the absolute value of the ratio of consecutive terms in the series.
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