Why are summation/product operators not much welcomed as being part of closed form expressions, even if they have finite terms?

Question

I read somewhere that in most closed form expressions, which are expressions used to calculate a certain outcome with only finite terms, summation/product operators are mostly neglected. I can understand if it was in case of infinite summations or multiplication, but even finite summations and prods are not considered closed form.

What is a suitable justification for that?

Answer 1

I would differentiate whether the number of terms in the variable is an absolute constant or a variable itself. So $\sum_{k=1}^n k$ is not a closed form expression, although it contains only finitely many terms. I would call $\sum_{k=1}^3 k$ a closed form expression, this is just a question of convenient notation (which is pointless in this specific example but could be useful in more complex situations).