A High-Precision Approximation to PI using an Arccosine Limiting Sequence

This paper introduces a closed-form transcendental formulation that converges monotonically to 𝜋. The expression is constructed by evaluating a base-10 sequence featuring a terminal digit 9 collapsing toward zero within the arccosine function. The formulation analytically converges to 𝜋 in the limit as the exponent index approaches infinity.