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Approximate the value of n for the formula (1-1/n)**n for which the difference between the value of n in the formula and 1/e is less than 0.0001.

How can we do using while and for loop in python .

I tried using while with the following code

from math import exp
value = 1/exp(1) # e being the exponential
n = 1;

while check < 0.0001:
    n=n+1
    formula = (1-1/n)^n
    check = value - formula
    if check <0.0001:
        print(n)

but since check is not defined before while the program doesn't run.

Is there any better solution?

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  • 1
    (1-1/n)^n doesn't do what you think it does. Commented Mar 16, 2017 at 20:05
  • use while True and break if condition on check is met; Commented Mar 16, 2017 at 20:06
  • Do you mean: (1-1/n)**n? Commented Mar 16, 2017 at 20:06
  • Yes ** is the correct one thanks Commented Mar 16, 2017 at 20:29

1 Answer 1

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1

Define check at the beginning, and replace ^ with **, as the latter one is the correct way to write power in python

import math
value = 1/math.exp(1) # e being the exponential
n = 1
check=1

while check > 0.0001:
    n=n+1
    formula = (1-1/n)**n
    check = value - formula

print(n)

By the way, ^ is the bitwise xor operator in python. You can look here for further description: http://python-reference.readthedocs.io/en/latest/docs/operators/bitwise_XOR.html

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