please use python 3

4330 Assignment 31 For this assignment, you need to submit a Python program for Problem 1. The file should be named: hw3-lastname.py Please: name your file in exactly this way; lowercase 'hw', a dash (not an underscore), and NO SPACES in the filename! You must complete this problem according to the "Structured Coding Pro- cess outlined at the end of this document. It will be graded according to that rubric. (1) (20 points) Suppose C > 1 is a real number, and consider the sequence {un} defined by uo = 1, un stom), 2 for r31 ribute Write a Python program which does the following: (i) Input a floating point number C greater or equal 1 from the user. (ii) Input a positive integer N from the user. (iii) Compute the term un of the sequence defined above, for the given values of C and N, and print it out with 8 decimal digits. Do NOT use a list or other data structure to store every term in the sequence. Note: it is not hard to prove that if lim Un exists, then it equals VC. It is a little more difficult, but also possible, to prove that this limit does exist for C > 1. 100 4330 A Structured Coding Process This describes the process that you are to apply to every assignment this semester, after the first two. It will be used as a grading rubric for your assignments as well. In particular, note that: 60% of the available credit does not depend explcitly on any programming at all. A program (working or not) without (I), (II), and (III) as described below can only earn up to 40% of the available credit. (I) Understand the problem (20%): Read and think about the problem description, and work out an example of your own choos- ing by hand. It should be a 'small' enough example that working it out by hand is reasonable, yet 'large enough to capture most things that you think might happen. Include this in com- ments at the top of your Python program file. (II) Develop an approach: (20%): Explain, in words, how to solve a general instance of the problem by hand. Include this in comments at the top of your Python program file. (III) Test your approach by hand: (20%): Take the method you just described, and apply it to a different example by hand. Verify that it works correctly. Include this in comments at the top of your Python program file. (IV) Code it: (20%): Translate your "in words method into Python code. (V) Test and debug: (20%): Attempt to use your code on the examples you already worked out by hand, and several more. Try hard to think of examples where something could fail. If it fails on any of those, determine whether the problem comes from (III) or (IV), by adding print statements, if necessary, and working the example by hand. You will be required to go through these steps for each assignment from Assignment 3 onward. You must clearly indicate what you've done for Steps (I), (II), and (III) in comments at the top of your Python program file. The code itself will be used to grade steps (IV) and (V)