APFIVE Maclaurin Series as a Function
The Maclaurin series $$\displaystyle \frac{x^2}{2} + \frac{x^4}{8} + \frac{x^6}{16} + \frac{x^8}{32} + \cdots = \sum_{n=1}^{\infty} \frac{x^{2n}}{2^n \cdot n}$$ converges to which of the following functions?
A
$$\frac{1}{2}\ln\left(\frac{2+x^2}{2}\right)$$
B
$$-\ln\left(1-\frac{x^2}{2}\right)$$
C
$$\frac{x^2}{2-x^2}$$
D
$$\ln\left(1+\frac{x^2}{2}\right)$$
Question Leaderboard
Not enough data yet to show leaderboard.