# Taylor Series

Let f = ln($\frac{1}{1-x}$)

show that if x $\in$ [-1/2 , 1/2] then

|f$^{n+1}$(x)| <= 2$^{n + 1}$ * n!

I am having a hard time seeing how 2$^{n + 1}$ * n! comes into play.

I have that the taylor series for f is $\Sigma$ $\frac{x^n}{n}$

If a take a derivative it becomes x^(n-1) and if I plug anything on the interval it is less than one. I am thinking that I did this wrong because of how big that upper bound is/.