Question

Write a program that approximates the value of pi. For a given n, the value of pi can be approximated by summing the terms in this series: 4 1 − 4 3 + 4 5 − 4 7 + 4 9 − 4 11 . . . .or by using the following formula:

p i = 4 ∑ k = 1 n ( − 1 ) k + 1 2 k + 1

Assume the value of n is provided by a user.

Answer 1

# pi_value.py

# most accurate value is at value n = 1000 
n = int(input("Enter value of n : "))

sum = 0
odd = 1

for i in range(n):

    # as we need to perform alternate
    # subtractions and addition
    # we consider even index for addition
    # odd index for subtraction
    if i%2==0:
        sum += (4/odd)
    else:
        sum -= (4/odd)
    
    odd += 2

    
print("Value of  pi : ",sum)

Output: