# Maclaurin Series

Calculus Level 2

A function $$f$$ is defined for all real numbers and satisfies $$f(0) = 1$$, $$f^{(1)}(0) = 0$$, $$f^{(2)}(0) = 0$$, $$f^{(3)}(0) = -1$$, $$f^{(4)}(0) = 0$$, and in general $$f^{(k)}(0) = (-1)^{k}$$ if $$k$$ is divisible by 3 and $$f^{(k)}(0) = 0$$ otherwise. What is the Maclaurin series of $$f$$?

 Clarification: In the answer choices, $$!$$ denotes the factorial function. For example, $$8! = 1\times2\times3\times\cdots\times8$$.

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