Maclaurin Series as a Function

Question

Which of the following functions is represented by the Maclaurin series $$\displaystyle \sum_{n=1}^{\infty} \frac{x^{2n}}{2^n \cdot n}$$?

Accepted Answer

$$-\ln\left(1-\frac{x^2}{2}\right)$$

Answer

$$\frac{1}{2}\ln\left(\frac{2+x^2}{2}\right)$$

Answer

$$\ln\left(1+\frac{x^2}{2}\right)$$

Answer

$$\frac{x^2}{2-x^2}$$

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