Finding the Nth Digit Of 'Pi'

There are multiple ways by which we can calculate the n^th digit of pi by using Arctan formula and Bailey–Borwein–Plouffe formula.
Chudnovsky Algorithm is a fast way of calculating the digits of pi and is similar to the arctan's formula.This formula is derived from the Ramanujan’s π formulae.
Here's the Formula :-

Simplifying further by solving the Fractional Power:

Dividing the series further into two parts a and b we get:


similarly,

we get,

we can calculate the next a term from the previous one, and the b terms from the a terms for simplifying the calculations.

Implementing the formula using Python

import math

def sqrt(n,m):
    m1=10**16
    m2=float((n*m1)//m)/m1
    b=(int(m1*math.sqrt(m2))*m)//m1
    n_m=n*m
    while True:
        a=b
        b=(b+n_m//b)//2
        if b==a:
            break
    return b

def power(n):
    if n==0:
        return 1
    r=power(n//2)
    if n%2==0:
        return r*r
    return r*r*10

def pi():
     m = power(100000)
     c = (640320**3)//24
     n = 1
     Ak = m
     Asum = m
     Bsum = 0
     while Ak != 0 :
          Ak *= -(6*n-5)*(2*n-1)*(6*n-1)
          Ak //= n*n*n*c
          Asum += Ak
          Bsum += n * Ak
          n = n + 1
          result = (426880*sqrt(10005*m,m)*m)//(13591409*Asum+545140134*Bsum)
          return result

stringPi = str(pi())
n = int(input())
print(stringPi[n-1])

This was the solution for GeeksForGeeks Problem.