I understand how to get the proper maclaurin series representation for $\cos x$, but I'm having trouble understanding the following part conceptually:
I get $\cos x$ as $\sum_{n=0}^\infty (-1)^n\frac{x^{2n}}{2n!}$ but,
Can the maclaurin series of $\cos x$ also be $\sum_{n=0}^\infty (-1)^n\frac{x^n}{n!}$?
I'm confused because even though the odd powers of this functions are going to $0$, wouldn't it still be valid to include them in our maclaurin series? Furthermore, why do we omit terms if they are $0$?