# Thread: Taylor Series of log(1-t)

1. ## Taylor Series of log(1-t)

Hello
How do you take the geometric/taylor (unsure which it is) series of log(1-t)?
I do already have a result given to me of 0 -t -(t^2)/2 -(t^3)/3 -(t^4)/4 -...
But don't know where its come from?
Also, I need to find log(1-t)-log(1-2t) in that form but getting different answers with my friend so would like some reassurement!
is it just (-t -(t^2)/2 -(t^3)/3 -(t^4)/4 -...) - (-2t -((2t)^2)/2 -((2t)^3)/3 -((2t)^4)/4 -... ?

2. Originally Posted by vjj
Hello
How do you take the geometric/taylor (unsure which it is) series of log(1-t)?
I do already have a result given to me of 0 -t -(t^2)/2 -(t^3)/3 -(t^4)/4 -...
But don't know where its come from?
Also, I need to find log(1-t)-log(1-2t) in that form but getting different answers with my friend so would like some reassurement!
is it just (-t -(t^2)/2 -(t^3)/3 -(t^4)/4 -...) - (-2t -((2t)^2)/2 -((2t)^3)/3 -((2t)^4)/4 -... ?
Do you know the expansion of $\frac{1}{1-t}$?

Can you see a way to get from that expansion to expansion of loge(1-t)?