Progressive Count of values

>Here< is an example spreadsheet of what I'm trying to do. I've posted on these other forums too: OzGrid, MrExcel

I need a way to count how many users there are with views during that or any previous week. This dataset is a typical example (though potentially hundreds of users and hundreds of weeks).

I'm not sure what formula to use here. I tried SUM with COUNT or COUNTIF, SUMPRODUCT, using array, but can't get it to work. I was able to manually create a new formula for each week that works but that's not useful for the size of the data I'm working with.

What formula should I use?

=sum(n(countif(offset($b3:b3,row(1:10)-1,),">0")>0)) cse

Thank you! This worked like a charm:
=SUM(--(MMULT(--$B3:B12,TRANSPOSE(COLUMN($B3:B12)^0))>0))

Another variation worked with slightly different syntax from @Carim on OzGrid was:
=SUM(N(MMULT(N($B$3:B12>0),TRANSPOSE(COLUMN($B$3:B12)^0))>0))

And another working solution from @pgc01 on MrExcel was:
=COUNT(1/FREQUENCY(IF($B$3:B$12<>"",ROW($B$3:B$12)),ROW($B$3:B$12)))

I couldn't get the suggestion from @tim201110 to work.