Wolfram Alpha != HP Prime CAS result: who is wrong?

[robve]

On Wolfram Alpha:
\( \sum_{k=0}^n k=\frac12n(n+1) \)
but it also says that:
\( \sum_{k=0}^{-10} k=0 \)
which surprised me, because the sign of \( n \) should not matter. What am I doing wrong here?

HP Prime CAS:
\( \sum_{k=0}^{-10}k=45 \)
which checks out \( \frac12(-10)(-10+1)=45 \)

So Wolfram Alpha thinks that \( \sum_{k=0}^{-10}k=0 \) is a so-called zero-trip loop? s=0; for (k=0; k<-10; ++k) s += k;

A couple of years ago, I spoke with a founder of Maple at a conference about similar problems and differences with program code as we were translating algebraic formulas in Prolog notation to FORTRAN to implement and run numerical solutions, and we knew these things can bite you. Their explanations of algebraic identities made sense back then and still do.

- Rob