CODEWITHSUNDEEP
python
LEJ2474
LEJ2474

Reputation: 43

Defining an error list for the convergence to pi

I'm new to python and I'm trying to model the convergence of a series towards pi based on a defined term. I've managed to create a list that returns the approximate value for pi at each iteration, however, I'm struggling to create a list that returns the difference between the approximation for pi and math.pi. I understand that the code is currently just looping the error term for one value of pi, and I don't know how to loop it over n values of pi. I'm sure it's a simple fix that I'm just overlooking so any help would be greatly appreciated. Here's my code:

from math import pi
from math import factorial

def term_in_series_1(n):
    values=[] 
    for k in range (n, -1,-1): #Here we are creating a for loop starting at n, finishing at -1 with a stepsize of -1
        value_of_term_n = 2 * 2**k * (factorial(k))**2 / factorial(2*k+1) #The loop uses this equation to calculate the value term of n for values in the range of n 
        values.append(value_of_term_n) #The append function allows each new value term of n to be added to the empty list "values" with length n
    return values

def series_1(n):
    approximation_for_pi = sum(term_in_series_1(n)) #This line is taking the sum of all the values in the series calulated in the previous function
    return approximation_for_pi

def error_1(j):
    values=[] 
    for i in range (j):
        for k in range (n):
            value_of_error_1 = pi - series_1(n) #The loop uses this equation to calculate the value term of n for values in the range of n 
            values.append(value_of_error_1) #The append function allows each new value term of n to be added to the empty list "values" with length n
        return values
error_1(15)

Upvotes: 0

Views: 64

Answers (1)

cdlane
cdlane

Reputation: 41872

This code seems to be the problem:

for i in range (j):
    value_of_error_1 = pi - series_1(n)

You have an iteration variable i but refer to n out of nowhere. Assuming the iteration variable should be n, here's a rework of your code:

from math import pi, factorial

def term_in_series_1(n):
    values = []

    for k in range(n, -1, -1):
        value_of_term_n = 2 * 2**k * factorial(k)**2 / factorial(2*k+1)
        values.append(value_of_term_n)

    return values

def series_1(n):
    return sum(term_in_series_1(n))

def error_1(j):
    errors = []

    for n in range(j):
        errors.append(pi - series_1(n))

    return errors

print(error_1(10))

Upvotes: 1

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