How can I use nested formulas in arrayfomula functions in google sheets? : I am new to posting in this community but have found solutions here many times.

I need google sheets to compute sums for each row using the arrayformula() function.

I know I can manualy enter somthing like;
=ARRAYFORMULA(A:A + B:B + C:C)

but I need the use of the functions to do it.

I've tried many things including;
=ARRAYFORMULA(sum(A:A,C:C))

Here is a sample file that I could use help with.

https://docs.google.com/spreadsheets/d/15ehNnTjAbuIUo_KNz363zLXjqlk-0InIspZAQm9yhB8/edit#gid=0

Thank you.