This have been asked on MSE but got no answers.

I'm searching for a proof that $\pi$ is irrational using a series representation for $\pi$, but can't find it.

However, on this wikipedia page show's that Apery's proof on the irrationality of $\zeta(3)$ can be simplified to apply on $\zeta(2)$ which is better than what i'm looking for because it shows that $\pi^2$ is irrational. But I can't find this proof either. If it's was done, maybe no one ever published.