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1. Determine whether the series is convergent or divergent. Σ n! 100n n=1

1. Determine whether the series is convergent or divergent. Σ n! 100n n=1

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Problem:** 1. Determine whether the series is convergent or divergent. \[ \sum_{n=1}^{\infty} \frac{n!}{100^n} \] **Explanation:** The series in question involves an infinite sum, where each term of the series is given by the formula \(\frac{n!}{100^n}\). Here, \(n!\) denotes the factorial of \(n\), which is the product of all positive integers up to \(n\). The denominator, \(100^n\), represents 100 raised to the power of \(n\). To solve this problem, you can use various tests for convergence, such as the ratio test or the comparison test, considering the factorial's rapid growth compared to the exponential term in the denominator.
Transcribed Image Text:**Problem:** 1. Determine whether the series is convergent or divergent. \[ \sum_{n=1}^{\infty} \frac{n!}{100^n} \] **Explanation:** The series in question involves an infinite sum, where each term of the series is given by the formula \(\frac{n!}{100^n}\). Here, \(n!\) denotes the factorial of \(n\), which is the product of all positive integers up to \(n\). The denominator, \(100^n\), represents 100 raised to the power of \(n\). To solve this problem, you can use various tests for convergence, such as the ratio test or the comparison test, considering the factorial's rapid growth compared to the exponential term in the denominator.
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