I have looked through the online literature and there seems to be conflicting answers to this question. Consider the finite sum
$$\sum_{i=0}^{\lfloor n/2 \rfloor} {n-1\choose i}$$
Is this expression considered closed-form?
These two links say that such a finite sum is not considered closed-form:
- https://opendsa-server.cs.vt.edu/ODSA/Books/CS3/html/Summations.html#:~:text=This%20is%20known%20as%20a%20closed%2Dform%20solution
- http://www3.govst.edu/wrudloff/CPSC438/CPSC438/CH05/Chapter5/Section.5.2.pdf
while this link says that such a finite sum is considered closed-form:
- https://en.wikipedia.org/wiki/Closed-form_expression#:~:text=Yes-,Finite%20sum,Yes,-Finite%20product
As far as I know, a closed-form expression has a finite number of standard operations or known functions. Based on this, my hunch is that the sum above is closed-form.