Hello everyone! Today we were asked to find the formula for the the Maclaurin Series expanion of the function , f(x)=\left\{\begin{matrix}\frac{x-\sin(x))}{x^3},if x\neq 0\\ \frac{1}{6}, if x=0<br /> <br /> <br />
\end{matrix}\right. (sorry about my piece wise ). Anyways, I don't have an idea to start this one with since this is a Maclaurin series yet I can't evaluate the nth derivative of the experession, \frac{x-sin(x))}{x^3} at x=0. By manipulations of the function \sin(x), \frac{x-sin(x))}{x^3}=\frac{1}{x^2}+\sum_{n=0}^{\infty} \frac{(-1)^{n+1}x^{2n-2}}{(2n+1)!}. From there, I am lost. Anyone have any idea on how I should proceed or better yet, how to do this the other way? Thanks everyone in advance!