Which of the following functions f(x)f(x)f(x) has a power series ∑n=0∞anxn\sum_{n=0}^{\infty} a_n x^n∑n=0∞anxn where an=sin(nπ/2)a_n = \sin(n \pi / 2)an=sin(nπ/2)?
f(x)=x1−x2f(x) = \frac{x}{1-x^2}f(x)=1−x2x
f(x)=x1+x2f(x) = \frac{x}{1+x^2}f(x)=1+x2x
f(x)=11+x2f(x) = \frac{1}{1+x^2}f(x)=1+x21
f(x)=x21+x2f(x) = \frac{x^2}{1+x^2}f(x)=1+x2x2