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The phrase "and the sum" is correct and usable in written English.
It can be used in contexts where you are discussing the total or aggregate of something, often in mathematical or financial discussions.
Example: "After calculating all the expenses, we found that the total cost, and the sum, exceeded our budget."
Alternatives: "and the total" or "and the aggregate".
Exact(58)
And the sum player B returns to player A is therefore a measure of reciprocity.
It's both its parts and the sum of it.
And the sum total of all this is improvement?
And the sum of those built up the reconstructed curve.
Because it advances technology and the sum total of human knowledge?
Her check appeared, and the sum was higher than she expected.
But they came together, and the sum became greater than the individual parts".
He also directed "Sneakers" and "The Sum of All Fears" and wrote "All of Me".
The time required to complete the test and the sum of errors were the dependent variables.
Similar(2)
Factor Graphs and the Sum-Product Algorithm.
Jump to February 2018 and the sum of Canadian peacekeepers is 40, half of them policemen.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com