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

AI Thread Summary
The discussion focuses on demonstrating that the Taylor series of (1+cx)ln(1+x) has terms that decay as 1/n^2 with an appropriate choice of constant c. A participant acknowledges the known decay of ln(1+x) as 1/n but struggles to show the desired result. There is also a side conversation about forum etiquette, with one user apologizing for being snappy and expressing a welcoming attitude towards newcomers. The thread highlights the importance of understanding series expansion and decay rates in mathematical analysis. Overall, the conversation emphasizes both the mathematical inquiry and the community dynamics within the forum.
optics101
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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
 
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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.
 
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