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Reciprocal Taylor Series

Calculus Level 3

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

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

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by Andrew Ellinor

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