Following up on my previous response.
I ran your code through tex4ht/xhmlatex with a small .cfg for html5+mathjax.
Your issues with tex4ht are these:
1. The summation sign is wrapped in an <mo> tag with the attribute
specification
mathsize="big". Get rid of that attribute specification.
2. The \centerdot is being typeset as U+25AA, ▪ "black small square",
where what
you probably want is U+22C5, ⋅ "dot operator". (This could be
circumvented in
the TeX source by using \cdot instead of \centerdot.)
-- Bill