Question

Write a program in Python that approximates the value of π by summing the terms of this series:

4/1-4/3 + 4/5- 4/7 + 4/9- 4/11 + ... The program should prompt the user for n, the number of terms to sum, and then output the sum of the first n terms of this series. Have your program subtract the approximation from the value of math. pi to see how accurate it is.

Answer 1

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#Import the math module.

import math

#Define the main()

#function.

def main():

    #Prompt the user to

    #enter the value of n.

    n = int(input("Enter the value of n: "))

   

    #Define teh required variables.

    calculated_pi_val = 0

    denominator = 1

    term_sign = 1

    #Run the loop to calculate

    #the sum of the first n

    #terms of the series.

    for i in range(n):

        #Add the next term to the series.

        calculated_pi_val += (term_sign*(4/denominator))

       

        #Increase the

        #denominator value by 2.

        denominator += 2

       

        #Change the sign

        #of the next term.

        term_sign *= -1

    #Calculate the error

    #in the approximated value.

    error = math.pi - calculated_pi_val

    #Display the calculated

    #value of pi.

    print("The calculated value"\

    " of pi is:", calculated_pi_val)

    #Display the error.

    print("Error in the calculated"\

    " value is:", error)

#Call the main()

#function.

main()