Reciprocal Taylor Series

Calculus Level 3

Determine the Taylor series for the function $f(x) = \frac{1}{x} \text{ centered at } x = 1.$

\sum_{n=0}^{\infty} \frac{(x - 1)^n}{n}

\sum_{n=0}^{\infty} (x - 1)^n

\sum_{n=0}^{\infty} (-1)^n(x - 1)^n

\sum_{n=0}^{\infty} \frac{(-1)^n(x - 1)^n}{n}