Taylor Series: Show Terms Decay as 1/n^2

Click For Summary

Discussion Overview

The discussion centers around demonstrating that the Taylor series of the function (1+cx)ln(1+x) has terms that decay as 1/n². Participants are exploring the mathematical properties of Taylor series and logarithmic functions, with a focus on the decay rates of the series terms.

Discussion Character

  • Exploratory, Technical explanation, Homework-related

Main Points Raised

  • One participant seeks assistance in showing that the Taylor series terms decay as 1/n², noting that ln(1+x) decays as 1/n but expressing uncertainty about the specific function in question.
  • Another participant reminds the original poster about forum rules regarding duplicate questions, indicating a need for adherence to community guidelines.
  • Subsequent posts involve apologies for earlier comments and clarifications about forum usage, with no direct contributions to the mathematical inquiry.

Areas of Agreement / Disagreement

The discussion does not reach a consensus on the mathematical question posed, as no solutions or methods have been provided to demonstrate the decay of the Taylor series terms.

Contextual Notes

Participants have not yet addressed the specific mathematical steps or assumptions needed to show the decay rate of the Taylor series terms, leaving the inquiry unresolved.

optics101
Messages
2
Reaction score
0
Show that, with an appropriate choice of constant c, the taylor series of

(1+cx)ln(1+x)

has terms which decay as 1/n^2

I know that ln(1+x) decays as 1/n, but I don't know how to show the above. Please help.

Thanks in advance
 
Physics news on Phys.org
It's against the forum rules to post the exactly same question in two different subforums. You should delete one of them.
 
My apologies, I am just beginning to use this forum. I did not know how to delete them, so I just cleared the content within the others.
 
The other copies are now deleted.
 
optics101 said:
My apologies, I am just beginning to use this forum. I did not know how to delete them, so I just cleared the content within the others.

By the way, welcome to the forum and I'm sorry I got a bit snippy there. I tend to do that (this is not a forum for the thinskinned) without thinking about significant things like, hey you're new here.

What's even worse is that after giving you a hard time I can't even answer your question. Fortunately for you, not everyone here is as useless as I am.
 

Similar threads

  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 10 ·
Replies
10
Views
6K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 9 ·
Replies
9
Views
3K
  • · Replies 17 ·
Replies
17
Views
4K
  • · Replies 19 ·
Replies
19
Views
4K
  • · Replies 3 ·
Replies
3
Views
3K