using a while loop to calculate arctan taylor series in python

Question

need to estimate arctan and subtract the current value from the last value. I'm very new to python and I have only this so far:

again==1
while again==1:
    x = float(input('enter tangent'))
    tolerance=input('enter reasonable tolerance')
    import math
    n=0
    while estimate-estimate>=tolerance:
        estimate=(-1**n)(x**(n+1))/(2n+1)
        n=n+1
        print(estimate)

    print(math.atan(x))
    difference=estimate-(math.atan(x))
    print(difference)
    again = int(input("do you want to run program again? yes = 1, no =0"))

How do I go about finding the difference between the current arctan value and the last value and how do I output the number of terms used?

Answer 1

For tangents between -1 and 1, try:

import math

again = 1
while again == 1:
    current_sum = 0
    previous_sum = 100
    x = float(input("enter tangent: "))
    tolerance = float(input("enter reasonable tolerance: "))
    n = 0
    while math.fabs(current_sum - previous_sum) >= tolerance:
        term = (-1) ** n * (x ** (2 * n + 1)) / (2 * n + 1)
        previous_sum = current_sum
        current_sum += term
        n += 1
    print(
        f"Actual={math.atan(x)}, Estimate={current_sum}, Number of Terms={n}"
    )
    again = int(input("do you want to run program again? yes = 1, no = 0: "))

Please note the use of extra variables and correction of errors in your Taylor Series formula.