finally A Simple code that worked after endeavors of nearly 6 hours

okay so first see this python code

"""

#STEP 1

x = 2

tol = 10**-5

ln15 = 0.40546511

n = 2

#STEP2

def pn(n,x):

sum = 0

for i in range(1,n+1):

sum = sum + (((-1)**(i+1))/i)*(x-1)**i

return sum

#STEP3

diff = abs(pn(n,2) - np.log(2))

while diff > 0.01:

n = n+1

diff = abs(pn(n,2)-np.log(2))

print(n)

np.log(2) """"

so this simple code took me nearly six hours of hard work but there was the error and infinite loop kept occurring again and again I don't know why but I was writing it with this exact same algorithm and I kept writing it again and even I had the solution as well but it was not working and finally it worked after executing it and comparing it with the solution at each line.

Message:- Don't Give up keep trying and try to start from the scratch there is always something hidden that we don't see.