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Let $\sum_{n=1}^\infty c_n (x-1)^n$ be the Taylor series of $f(x)=\ln x$ at $x=1$ (the series starts at $n=1$ since $f(1)=0$).

What is the expression for the $n$th coefficient $c_n$?

$\cfrac{1}{n}$

$\cfrac{1}{n!}$

$\cfrac{(-1)^n}{n}$

$\cfrac{(-1)^n}{n!}$

$\cfrac{(-1)^{n+1}}{n}$