In class the other day, the multivariate series for the last example was
\[\sum_{(x,y)} x^2y + y^3x\]was supposed to be
\[\sum_{(x,y)} x^2y + 3\]don’t know where that one came from, silly note error. The domain of summing is $\lbrace 1,…10\rbrace \times \lbrace 2,…,5 \rbrace$. We’ll talk more about derivatives for things like this one in discussion.