# https://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80
"""
Pi is an irrational number having non-recurring decimal values. We commonly know Pi=3.14 or Pi=22/7, but it is just an approximation for our ease. There are two methods to calculate the value of pi in python:

Method 1: Using Leibniz’s formula

The formula is –

X = 4 - 4/3 + 4/5 - 4/7 + 4/9 - ....

This series is never-ending, the more the terms this series contains, the closer the value of X converges to Pi value.

Approach:

    Initialize k=1 // this variable will be used as the denominator of leibniz’s formula, it will be incremented by 2
    Initialize sum=0 // sum will add all the elements of the series
    Run a for loop from 0 to 1000000 //at this value, we get the most accurate value of Pi
    Inside for loop, check if i%2==0 then do sum=sum+4/k
    Else, do sum=sum-4/k
    Increment k by 2, go to step 3
"""

# Initialize denominator
k = 1

# Initialize sum
s = 0

for i in range(1000000):

    # even index elements are positive
    if i % 2 == 0:
        s += 4 / k
    else:
        # odd index elements are negative
        s -= 4 / k

    # denominator is odd
    k += 2

print(s)