Question

Using Java's Biglnteger / BigDouble import java.math), Python, solve the following algorithm by Ramanujan and Chudnovsky in solving the approximate value for Pl.. Invoke two separate methods to calculate each algorithm. Take the value of n up 100000. Ramanujan's Formula for Pi First found by Ramanujan. It's my favourite formula for pi. I have no idea how it works. (4n)! 26390n + 1103 396an 9801 (n!)4 Other formulas for pi: A Ramanujan-type formula due to the Chudnovsky brothers used to break a world record for computing the most digits of pi: (6n)! Σ-1). n!3(3n)! 13591409 + 545140134n 6403203n 53360 v640320 n-0 For implementations, it may help to use 640320 = 8 · 100100025 - 327843840

Answer 1

Ans:

Initially calculate the factorial of n:

def fact(n):
if n == 0:
return 1
else:
factorial = fact(n-1)
ans = n * factorial
return ans

Then calculate the value for pi using the below function:

def pi_value():
total = 0
i= 0
first_term = 2 * math.sqrt(2) / 9801
start = True
while start == True:
numerator = float(fact(4*i) * (1103 + 26390 * i))
denominator = float(fact(i)**4) * 396**(4*i)
final_term = first_term * float(numerator/denominator)
total =total+ final_term
i =i + 1
if final_term < 1e-15:
start == False
print("The value of pi is:" )
break
return 1 / total

print(pi_value())
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Output

import math Window Help Python 3.6.5 (v3.6.5:f59c0932b 4, Mar 28 2018, 17:00:18) [MSC v.1900 64 bit (AMD64)] on win3 def fact (n): if n == 0: return i else: factorial = fact (n-1) ans = n * factorial return ans Type "copyright", "credits" or "license ()" for more informati on >>> ===== RESTART: C:\Users\user\Desktop\yy.py == The value of pi is: 3.141592653589793 >>> def pi_value(): total = 0 i= 0 first_term = 2 * math.sqrt (2) / 9801 start = True while start == True: numerator - float (fact (4*i) * (1103 + 26390 * i)) denominator = float (fact(i)**4) * 396** (4*i) final_term = first_term * float (numerator/denominator) total =totalt final_term i =i + 1 if final term< le-15: start == False print("The value of pi is:") break return i / total print (pi_value())