Question

Question about pointwise converge of Series of Functin

fn:A-->R

we know that the series is pointwise convergent if limit of the partial sum Sm=f

However, I am wondering the format is Sm(x)=f1(x)+f2(x).....+fm(x)

What is the meaning of "x" ?   and does that mean every fixed x in A of the partial sum of the series need to be convergent?

Example, limit Sm=f1(x1)+f2(x1)+f3(x1)....fm(x1)

limit Sm=f1(x2)+f2(x2)+f3(x3).....fm(x2)

every x in A needs to be convergent?

Answer 1