1. Let's first state the problem clearly: You want to know if a given series is a Maclaurin series or a Taylor series. 2. A Taylor series is an expansion of a function $f(x)$ around a point $a$, given by the formula: $$f(x) = \sum_{n=0}^\infty \frac{f^{(n)}(a)}{n!} (x - a)^n$$ where $f^{(n)}(a)$ is the $n$th derivative of $f$ evaluated at $x=a$. 3. A Maclaurin series is a special case of the Taylor series centered at $a = 0$: $$f(x) = \sum_{n=0}^\infty \frac{f^{(n)}(0)}{n!} x^n$$ 4. Therefore: - If the series is expanded around $x=0$, it is a Maclaurin series. - If the series is expanded around any point $x=a \neq 0$, it is a Taylor series. 5. In conclusion, without a specific center point $a$, you cannot distinguish between the two by name alone. If the center is $0$, it is Maclaurin; otherwise, it is Taylor.