What is a closed form solution?

[docnet]

TL;DR

What is the definition of a closed form solution in math? Where did the term originate? When is it preferred?

Hi friends, I was wondering if you could give the definition of 'closed form', with examples of closed form solutions and open? form solutions.

Foe example, is this a closed form solution?
$$\sum_{k=1}^\infty \frac{1}{2^k}$$

Or this?
$$\sum_{k=1}^5 \frac{1}{2^k}$$

Thanks.

 

[PeroK]

Try this to get you started:

https://mathworld.wolfram.com/Closed-FormSolution.html