The following problems below require the utilization of recursion to be solved. Must also have comments. Write a python program that compute the geometric sum of n-1 with n=1 to positive infinity. Write a python program the computes the harmonic sum of n-1.

python 3 Write a program that lists all ways people can line up for a photo (all permutations of a list of strings). The program will read a list of one word names, then use a recursive method to create and output all possible orderings of those names, one ordering per line. When the input is: Julia Lucas Mia then the output is (must match the below ordering): Julia Lucas Mia Julia Mia Lucas Lucas Julia Mia Lucas Mia Julia Mia Julia Lucas Mia Lucas Julia question: is it any way that i can use ('if' statement as base case, and 'else' statement as recursive case) in the code below? thanks. code: def all_permutations(permList, nameList):# TODO: Implement method to create and output all permutations of the list of names.def createPermutationsList(nameList):f = len(nameList) if f == 0:return [] if f == 1:return [nameList] permList = [] for i in range(f):newList = nameList[i]remaining = nameList[:i] + nameList[i+1:]for p in createPermutationsList(remaining):permList.append([newList] + p)…

IN PYTHON, Using recursion: ask the user for the length of a square and the character they want to use. Draw the square (similar to mini assignment #15 in functions part 3). Once the user creates the square with their specification, ask them if they want it to be smaller or larger and how many times. Draw all the squares growing in size to the specified range.

Convert Newton's method for approximating square roots in Project 1 to a recursive function named newton . (Hint: The estimate of the square root should be passed as a second argument to the function.) An example of the program input and output is shown below: Enter a positive number or enter/return to quit: 2 The program's estimate is 1.4142135623746899 Python's estimate is 1.4142135623730951 Enter a positive number or enter/return to quit

1.)I have to recursive with python language and was asked to do a buy 2 get 1 free where you have some amount of money(x) each item costs a given amount(y), for each 2 item you get 1 free, builda recursive solution to find out how many items you can buy for x amount of money. 2.) Buy M, get N free Then alter your first answer to allow for the user to enter any M and N for how many you need to buy to get free items

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