Summations with backwards limits

I have a sum defined as
$\sum_{\mu=0}^{k-1} f(\mu)$
, what does it mean in the case that $k=0$? Then I have a sum running from $0$ to $-1$ which I suppose doesn't make sense? Wolfram alpha gives $0$ no matter what I put in for $f(\mu)$, why is this the case?

I think I have a better understanding of what this means in the context of integrals, but summations not so much. Is there a connection?