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

optics101 · Oct 12, 2011

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

phinds · Oct 12, 2011

It's against the forum rules to post the exactly same question in two different subforums. You should delete one of them.

optics101 · Oct 12, 2011

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.

Mark44 · Oct 12, 2011

The other copies are now deleted.

phinds · Oct 12, 2011

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.

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

Discussion

Similar threads

High School Can We Simplify the Taylor Series Expansion for e^(f(x,y))?

Undergrad Taylor series of 1/ln(t+1) at t=0

Using Standard Taylor Series to build other Taylor Series

Undergrad Which x_0 to use in a Taylor series expansion?

Undergrad Different series than Taylor series for a function

Undergrad Taylor series to evaluate fractional-ordered derivatives

Undergrad Questions about this video on Taylor series

Undergrad Can Taylor series be used to get the roots of a polynomial?

Undergrad Convergence of Taylor series in a point implies analyticity

Undergrad How do I evaluate the Taylor series for ##Si(x)## around a given value?