I happened to come across Taylor series and Maclaurin series recently, but everywhere I read about the expansion for $ ln(1+x)$ , it was stated that the approximation is valid for $ -1 < x < 1$ .

I understand that the bounds for $ x$ are because the series doesn’t converge for $ |x|>1$ , but is there any equivalent of this series for the value of $ |x|$ as greater than $ 1$ ?

Please note that I am not asking if we can compute for $ |x|>1$ or not, as that can be done by computing for $ \frac 1x$ , which will then lie between $ -1$ and $ 1$ .

Also, I’m quite new to all this, so new that today was the day I read the name ‘Maclaurin’ for the first time. So any answers understandable with high school mathematics are highly appreciated.

Thanks!