Let's say I have a list of arguments, of any length.
How would I add them all together?
f = Evaluate[Plus @@ Array[Slot, 3]] &
f[1, 2, 3]
This would add together 3 numbers, but how would I add together any amount of numbers?
See SlotSequence. I would use:
f = +## &
f[1, 2, 3]
6
The long form:
InputForm[f]
Plus[##1] &
Other forms would be:
Total @ {##} &
Tr @ {##} &
Plus @@ {##} &
I'm not sure I'm interpreting your question correctly, but the most obvious way is just
f = Plus;
f[1, 2, 3, 4, 5]
I assume that there is a deeper use case behind your question, so when you clarify what you like to achieve, maybe someone can give you better tips.