I want to create a pi calculator with no limit to precision, but I cannot find a formula for finding only the digit number n of pi. Here is what I mean:
Let's say I want to find the 4th digit of pi. Since $\pi\approx3.14159...$ then the digit number 4 of pi is 5, because that is the 4th digit that comes up after the decimal point.
Most formulas like series such as this one: $\pi+3=\sum_{n=1}^{\infty}(\frac{n2^{n}n!^{2}}{\left(2n\right)!})$ are limited by how precise the calculator is, and it isn't what I am looking for unfortunately.
Big thanks to anyone who can help!