QUESTION $13$

On some suitable interval, a power series representation of the function $f(x)=\frac{x^2}{2x^3+1}$ is given by

A$.{\displaystyle \underset{n=0}{\overset{}{}}}(-1{)}^n{2}^n{x}^{n+2}$

B$.{\displaystyle \underset{n=0}{\overset{}{}}}(-1{)}^n{2}^n{x}^{3n+2}$

C$.{\displaystyle \underset{n=0}{\overset{}{}}}{2}^n{x}^{3n+2}$

D$.{\displaystyle \underset{n=0}{\overset{}{}}}(-1{)}^n{2}^n{x}^{3n+3}$

E$.{\displaystyle \underset{n=0}{\overset{}{}}}(-1{)}^n{2}^n{x}^{3n}$