# Math Help - subtraction of series

1. ## subtraction of series

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

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

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

Is this valid $\frac {e^x -\cos x}{x} =$ $\sum \frac {x^{n-1}}{n!}-\frac{(-1)^nx^{2n-1}}{(2n)!}$
Yes it's valid.

3. They probably want you to simplify it?

4. The reason why its valid is that both series converge for all x.