Micro-challenge: Special Event

[Albert Chan]

(12-26-2022 02:00 PM)Thomas Klemm Wrote:  \(
\begin{align}
\pi = 2 + \frac{1}{3}\left(2 + \frac{2}{5}\left(2 + \frac{3}{7}\left(2 + \cdots \right)\right)\right)
\end{align}
\)

Thus we can write in this specific basis: \(\pi = 2.2222\cdots\).

How does this identity derived?

BTW, there was a typo, the number have no radix point.
Here is APL, with 50 2's, decoded with variable radix on the left

      {(⌽⍵÷1+2×⍵)⊥(2+0×⍵)}⍳50
3.141592654