[mkl]

Continuing the pattern it's

  $\pi = 3 + \sum_{k=1}^\infty 3 \frac{(2k-1)!!}{(2k)!!} \frac{1}{2k+1} \frac{1}{4^k}$ [1].

n!! is double factorial, the product of odd or even numbers up to n (depending on whether n is odd or even) [2].

Edit: added a simpler series from https://math.stackexchange.com/a/14116:

  $\pi = \sum_{k=0}^{\infty} \frac{(2k)!!}{(2k+1)!!} \left(\frac{1}{2}\right)^{k-1}$

[1] https://imgur.com/a/YtA8kUx

[2] https://en.wikipedia.org/wiki/Double_factorial