This series converges even when x = 1 and since we know that arctan (1) = π/4, we then get the infinite series representation That's pretty cool. Unfortunately, it's not that efficient.

Moving beyond polygons The development of infinite series techniques in the 16th and 17th centuries greatly enhanced people’s ability to approximate pi more efficiently. An infinite series is ...

Finding pi. _Synopsis palmariorum matheseos_ In the pages of his Synopsis, Jones also showed his familiarity with the notion of an infinite series and how it could help calculate pi far more ...