How can I simplify error estimates for a given equation?

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Homework Help Overview

The discussion revolves around simplifying an expression related to error estimates in a mathematical context, specifically involving sequences and convergence. The participants are examining an equation that includes terms with subscripts and powers, indicating a focus on analysis within a calculus or numerical methods framework.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to simplify a complex expression involving error terms. There are questions regarding the correctness of initial attempts and the need to express the result in terms of the error variable, e_n. Some participants are seeking clarification on what specifically needs to be addressed in the simplification process.

Discussion Status

The discussion is ongoing, with participants providing feedback on each other's attempts. There is a focus on identifying issues in the initial solutions and clarifying the requirements for simplification. No consensus has been reached yet, and multiple interpretations of the problem are being explored.

Contextual Notes

Participants have noted the importance of expressing the result in terms of e_n for further analysis regarding convergence. There is also a reference to a visual aid that may provide additional context, though it is not directly accessible within the thread.

MelissaHerr
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Homework Statement


Simplify: 1/k [(k-1) x_n+ x^k/(x_n^(k-1) )]- 1/k [(k-1)x+ x^k/x^(k-1) ] where e_n = x_n - x

x_n means x subscript n
e_n means e subscript n

It might be easier to look at the picture I typed out in MS Word.
https://www.flickr.com/photos/135306726@N08/22156107431/in/dateposted-public/

Homework Equations

The Attempt at a Solution


I only got [(k-1)/k]e_n + x^k/k (1/x_n^(k-1) - 1/x^(k-1))

Please help!
 
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Please help!
 
MelissaHerr said:

Homework Statement


Simplify: 1/k [(k-1) x_n+ x^k/(x_n^(k-1) )]- 1/k [(k-1)x+ x^k/x^(k-1) ] where e_n = x_n - x

x_n means x subscript n
e_n means e subscript n

It might be easier to look at the picture I typed out in MS Word.
https://www.flickr.com/photos/135306726@N08/22156107431/in/dateposted-public/

Homework Equations

The Attempt at a Solution


I only got [(k-1)/k]e_n + x^k/k (1/x_n^(k-1) - 1/x^(k-1))

Please help!

Help how? What is wrong with your solution? (I have not checked the details, so you will need to tell me!)
 
Ray Vickson said:
Help how? What is wrong with your solution? (I have not checked the details, so you will need to tell me!)
It needs to be simplified into some form of e_n, so that I can use it to determind if it will converge.
 
Ray Vickson said:
Help how? What is wrong with your solution? (I have not checked the details, so you will need to tell me!)
e_(n+1) = x_(n+1) - x
= 1/k [(k-1) x_n+ x^k/(x_n^(k-1) )]- 1/k [(k-1)x+ x^k/x^(k-1) ]
 

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