Write a function estimatePi() to estimate and return the value of Pi based on the formula found by an Indian Mathematician Srinivasa Ramanujan. It should use a while loop to compute the terms of the summation until the last term is smaller than 1e-15. The formula for estimating Pi is given below:
As per Ramanujam's estimation
(I'm sorry, I'm unable to upload the image)
def estimatePi():
import math
def factorial(n):
if n == 0:
return 1
else:
return n * factorial(n-1)
k=0
final=0
pi=0
while pi<1e-15:
a=factorial(4*k)
b=(1103+26390*k)
c=factorial(k)
d=c**4
e=396**(4*k)
f=2*math.sqrt(2)/9801
final+=(a*b*f)/(d*e)
k+=1
pi=1/final
return pi
and, my problem is this: Expected answer was =3.14159265359 my answer is =3.14159273001
I was not able to find my fault :(. Can anyone help with this for me?
You answer is correct. Float numbers have problems with accuracy especially for large number of digits after the decimal point; and when calculating non-exact values.
You can see from your answer that it has estimated the value of pi correctly for 5 digits after the decimal.