Question

I have a python coding question:

Write the function: eAapproximately (n), that takes a positive integer value n and returns an approximation of e as (1 + 1/n)^n

I am not even sure what the question is asking me to do but I think it is asking me to code that function. Does anyone know how to do this?

Answer 1

#python code please do care of indentation

#save code 'xyz.py'

#run 'python xyz.py'

#for explanation see screenshots added

#########################################################################
#   eApproximation(n):   takes positive no. as n           #
#       calculate the value of given formula           #
#       (1 + 1/n)^n as an approximation of e           #
#                                   #
#   if you see that what is e?                   #
#       The number e is a famous irrational number, and is one #
#       of the important numbers in mathematics.       #
#       The first few digits are:               #
#           2.7182818284590452353602874713527       #
#       It is often called Euler's number           #
#                                   #
#   Basically this question is asking that use that given formula   #
#   and calculate the approximation of 'e'.               #
#   If you increase the value of n than this formula gives better   #
#   approximation of e.                       #
#                                   #
#                                   #
#   lim[n->infinity](1 + 1/n)^n = e                   #
#                                   #
#   if the value of n->infinity then formula gives exact value of   #
#   e. Here we need to write a python code which will calculate   #
#   the value of e using that formula.               #
#   for further explanation see the screen shot added       #
#########################################################################

def eApproximation(n):
   x = float(n)
   e = (1 + 1/x)**x
   return e

print("(n, e)")
for i in [1,2,5,10,100,1000,10000,100000]:
   print(i, eApproximation(i))