Maclaurin Series from a Geometric Series

Question

Given the geometric series representation $$\displaystyle \frac{1}{1-x} = \sum_{n=0}^{\infty} x^n = 1 + x + x^2 + x^3 + \cdots$$ for $$|x| < 1$$, which of the following is the Maclaurin series for $$g(x) = \frac{x^2}{1-x^3}$$?

Accepted Answer

$$\displaystyle \sum_{n=0}^{\infty} x^{3n+2}$$

Answer

$$\displaystyle \sum_{n=1}^{\infty} nx^{3n+1}$$

Answer

$$\displaystyle \sum_{n=0}^{\infty} x^{2n+3}$$

Answer

$$\displaystyle \sum_{n=2}^{\infty} x^{3n}$$

Maclaurin Series from a Geometric Series

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