Explanation Given : b n = n ! π n Formula Used : Squeeze Theorem Calculation : Step 1: For n ≥ 4 , let d n = 4 n n ! = 4 1 . 4 2 .... 4 4 ︸ call this C . 4 5 . 4 6 ..... 4 n − 1 . 4 n ︸ Each factor is less than 1 Then clearly, 0 ≤ 4 n n ! ≤ C . 4 n since each factor after the first four is < 1...

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Chapter 11.1, Problem 62E

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To calculate: The limit of the sequence $b_{n} = \frac{n!}{π^{n}}$ or show that it diverges using the appropriate limit laws and theorems

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Chapter 11.1, Problem 61E

Chapter 11.1, Problem 63E

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Chapter 11 Solutions

CALCULUS W/SAPLING ACCESS >IC<

Ch. 11.1 - Prob. 1PQ Ch. 11.1 - Prob. 2PQ Ch. 11.1 - Prob. 3PQ Ch. 11.1 - Prob. 4PQ Ch. 11.1 - Prob. 5PQ Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E

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The limit of the sequence b n = n ! π n or show that it diverges using the appropriate limit laws and theorems

Solution Summary: The author explains how the squeeze theorem calculates the sequence bn = n, and shows that it diverges using appropriate limit laws.

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To calculate: The limit of the sequence $b_{n} = \frac{n!}{π^{n}}$ or show that it diverges using the appropriate limit laws and theorems

Want to see the full answer?

Chapter 11 Solutions

The limit of the sequence b n = n ! π n or show that it diverges using the appropriate limit laws and theorems

Solution Summary: The author explains how the squeeze theorem calculates the sequence bn = n, and shows that it diverges using appropriate limit laws.

Concept explainers

Videos

To calculate: The limit of the sequence bn=n!πn or show that it diverges using the appropriate limit laws and theorems

Want to see the full answer?

Chapter 11 Solutions

To calculate: The limit of the sequence $b_{n} = \frac{n!}{π^{n}}$ or show that it diverges using the appropriate limit laws and theorems