How can I simplify error estimates for a given equation?

[MelissaHerr]

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!

 

[MelissaHerr]

Please help!

 

[Ray Vickson]

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!)

 

[MelissaHerr]

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.

 

[MelissaHerr]

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) ]