'Iterable Sum over row in google sheets?

I have data in google sheets, looking like this:

A B C D E F G
TP 14656 18885 14317 19312 13303 14311
FN 12216 20107 14066 16323 11180 3478

and I want to implement the following formula:

formula

which would manually look like this:

=(B1/(B1+B2))+(C1/(C1+C2))+...+(G1/(G1/G2))

However, I need this formula to be scalable. I've tried to use ARRAYFORMULA and SERIESSUM but could not manage to actually iterate over the row. Does sheets even support this, and if so, how does sheets implement iterating sums?



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