Ratio Test for Series Homework: Author's Solution & Attempt at a Solution

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Homework Help Overview

The discussion revolves around the Ratio Test for series, specifically addressing the author's solution and the original poster's attempt at understanding the series' denominator.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the nature of the denominator in the series, questioning whether it can be represented as (2n + 1)!. There is a focus on clarifying the distinction between factorial notation and the product of odd integers.

Discussion Status

The discussion is active, with participants engaging in clarifying the definitions and assumptions regarding the series' denominator. Some guidance has been offered regarding the differences between factorials and products of odd integers.

Contextual Notes

There is a noted discrepancy in understanding the series' denominator, with participants emphasizing the importance of correctly interpreting the mathematical expressions involved.

Bashyboy
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Homework Statement


I attached a file that includes the author's solution, and some of my work.


Homework Equations





The Attempt at a Solution

 

Attachments

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Bashyboy said:

Homework Statement


I attached a file that includes the author's solution, and some of my work.


Homework Equations





The Attempt at a Solution


The denominator in the series is not (2n + 1)! It is the product of the odd integers from 1 to 2n + 1.
 
But can't you write that as (2n + 1)! ?
 
No, not at all.
(2n + 1)! = 1 * 2 * 3 * ... * (2n - 1) * (2n) * (2n + 1)

Your expression skips all the even integers.

A simple example is 5! vs. 1 * 3 * 5. Clearly they aren't equal.
 

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