Question

Is this set closed:

A closed set is if there exists no limit points of that set that isn't an element of that set.

Basically if there's a limit point that's not contained in that set, it's not closed.

Answer 1

\[A = \left\{ \frac{1}{1^{2}} + \frac{1}{2^{2}} + ... + \frac{1}{n^{2}} , \forall n \in \mathbb{N} \right\}\]

Answer 2

I got it.
The summation of 1/n^2 converges, so let that number be x, then x is limit point of A, but not in A, so it's not closed set.