For example does $$\sum_{n=-\infty}^{-1}\frac{1}{n^2}=\sum_{n=1}^{\infty}\frac{1}{n^2}$$ Or does $$\sum_{n=-\infty}^{0}\frac{1}{\sin^2(n\pi+\frac{1}{2}\pi)}=\sum_{n=0}^{\infty}\frac{1}{\sin^2(-n\pi+\frac{1}{2}\pi)}$$
My guess is that it is true but I have no idea how to go about proving it.
$\textbf{EDIT:}$ Sorry I had not meant to cause confusion over a reordering of the terms. I was using the notation used when encountering summands such as $$\sum_{-\infty}^{\infty}$$ and was not trying to infer that I wanted to start the sum at $-\infty$. Thanks!