Sum over a formula in Google Sheets

I have a Google Sheet and I need to add a lot of stuff like

(ABS(A1)+A1)/A1+ (ABS(A2)+A2)/A2+...+ (ABS(A10)+A10)/A10

but I don't want to write out the sum each time for each term A1,A2,A3,..., A10

Is there a way to write the sum more concise? like

SUM( (|x| + x)/x : for x from A1 to A10) 

I know that's not correct but that is what I want.