I know you can multiple series but if you want to find the series for $\displaystyle e^x -\cos x$ can you subtract two known series.

Is this valid $\displaystyle \frac {e^x -\cos x}{x} =$ $\displaystyle \sum \frac {x^{n-1}}{n!}-\frac{(-1)^nx^{2n-1}}{(2n)!}$