Expanding taylor series using relation between successive terms with a specified tolerance in spyder

Question

I have used this code to determine the value of e^pi with a specified tolerance in spyder(Python 3.8).

from math import*
term=1
sum=0
n=1
while (abs(e**pi-term))>0.0001:
    term=term*pi/n
    sum+=term
    n+=1
print(sum,e**pi)

I ran this code several times. But spyder is not showing anything when I run this code. I am new to python. So now I have no way to know whether this code is correct or not. It would be beneficial if you could verify whether this code is valid or not.

Answer 1

The while loop does not end.

I have stuck in a condition to break out of the loop (at 10,000 cycles) to show this:

from math import*
term=1
sum=0
n=1

while (abs(e**pi-term))>0.0001:
    term=term*pi/n
    sum+=term
    n+=1
    if n > 10_000:
        print('large n')
        break
print(sum,e**pi)

If you replace the while loop with a for loop, then you can see each iteration as follows.

term=1
sum=0

for n in range(1, 101):
    term=term*(math.pi)/n
    sum+=term
    print(n, sum, math.e**math.pi)

And this is the result for the first 10 items:

1 3.141592653589793 23.140692632779263
2 8.076394854134472 23.140692632779263
3 13.244107634184441 23.140692632779263
4 17.30281976060121 23.140692632779263
5 19.852983800478555 23.140692632779263
6 21.188246569333145 23.140692632779263
7 21.787511098653937 23.140692632779263
8 22.02284172901283 23.140692632779263
9 22.104987615623955 23.140692632779263
10 22.13079450701397 23.140692632779263

The numbers are getting larger, hence the while loop was never exited (and your laptop probably got quite hot in the process !!).