Python: Approximating Ln(x) Using Taylor Series

I'm trying to build an approximation for ln(1.9) within ten digits of accuracy (so .641853861). I'm using a simple function I've built from ln[(1 + x)/(1 - x)] Here is my code so

Solution 1:

The principle is;

• Look at how much each iteration adds to the result.
• Stop when the difference is smaller than 1e-10.

You're using the following formula, right;

(Note the validity range!)

def taylor_two():
    x = 1.9 - 1
    i = 1
    taySum = 0while True:
        addition = pow(-1,i+1)*pow(x,i)/i
        ifabs(addition) < 1e-10:
            break
        taySum += addition
        # print('value: {}, addition: {}'.format(taySum, addition))
        i += 1return taySum

Test:

In [2]: print(taylor_two())
0.6418538862240631

In [3]: print('{:.10f}'.format(taylor_two()))
0.6418538862