Q:

Is it always true that no closed forms exists for any divergent series?

Having seen many questions regarding finding closed form of integrals or infinite series, and some users providing either the final answer or detailed solution, and also reading how one finds a closed form of an equation
How do people on MSE find closed-form expressions for integrals, infinite products, etc?
Some users are mind bogglingly skilled at integration. How did they get there?
After the MSE suggestions popped up when typing the question, it seems this question is an extension of this one
Is there an algorithm to determine if a closed form solution exists?
which was known to be there are no known ways to detect the existence of close forms for any general mathematical expression

(maybe a stupid subquestion, but I have seen many weird exceptional things in maths thus starting to wonder)
is it always true that no closed forms exists for any divergent series?

A:

The divergent series
$$\sum_{i=1}^n 1$$
has the closed form
$$n$$
That was so easy I doubt that was your actual question.

