By applying the variational approach and then comparing the result to the exact solution, we can calculate the error in the approximation. That is the main and major use of Terminal notation of pi.
π/2 = [tex] \lim_{n \to \infty} π (2j)(2j) / (2j-1)(2j+1)
Here, by this expression, we set the limits, and get the approximate error in the experiment.
Hope this helps!