Variable not redefining correctly in for loop (Python)

Question

I need to create a function that correctly computes E _m as E _m = 1 - mE _m-1

I'm having some issues figuring out why my variable isn't returning the correct values. Here is a summary of the problem I am tackling

Write a function called integration that takes as input the integer m and, using the algorithm described below, returns the value of E_m . Make certain that you index this correctly, ie E ₀ = 1 − 1/e not E1 = 1 − 1/e. Be very careful with how Python indexes if you try to do this as an indexed array.

Set E = 1 - 1/e
    for j = 1, ... , m do
        E = 1 - j*E
    end for
    return E

Here is my code

import numpy as np
def integration(m):
  E_m = 1 - 1/np.e
  for j in range(m):
    E_m = 1 - j*E_m
  return E_m

My code, if m > 0 , returns the wrong answer (for example integration(1) returns 1 , when it should be 1 - 1*(1-1/e) ). The text seems to indicate that I should use an array, but I don't see why I would need to. Why isn't my code redefining my variable E_m correctly? I'm new to Python, so I'm not sure if it's a problem with having the variable name in the redefinition or not.

Answer 1

Python loops start with 0 and are non-inclusive. Try range(1, m+1)