Michael Watts Michael Watts - 1 year ago 116
Python Question

Python Iteration Homework

I have 2 questions I need to ask for help with. One question I don't entirely understand so if someone could help me to that would be great.

Question One (the one I don't entirely understand):

One definition of e is

Formula for e

This can be calculated as my_e = 1/math.factorial(0) + 1/math.factorial(1) + 1/math.factorial(2) + 1/math.factorial(3) + …

Let n be the input number of the math.factorial() function. n successively takes on 0, 1, 2, 3 and so on. Find the smallest n such that the absolute value of (my_e – math.e) is less than or equal to 10-10. That is, abs(my_e - math.e) <= (10 ** -10).

I just don't entirely understand what I am being asked to do. Clarification would be great. Thanks!

Question 2:

Ask the user to type in a series of integers. Sum them up and print out the sum and the number of integers the user has entered.

My code

So what should happen is after I enter the numbers I want to enter and hit the enter key, it should calculate and print out "sum = 25 count = 3". The screenshot shows what error message I am getting.

Any help you have is welcomed and greatly appreciated.

Answer Source

As far as you first question goes:

>>> import math
>>> math.e
>>> sum(1.0/math.factorial(i) for i in range(5))
>>> abs(sum(1.0/math.factorial(i) for i in range(5)) - math.e) < 10**-10
>>> abs(sum(1.0/math.factorial(i) for i in range(30)) - math.e) < 10**-10

So, somewhere between n == 5 and n == 30 you get 10 decimal places for e. Create the sum term by term in a while-loop (instead of by using the sum function as I have, since you are unlikely to have seen that syntax yet). At each pass through the loop, compare the sum with math.e. Stop when you get the target accuracy. Return the final n.

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