Problem 2 [13 pts]: Algorithms and Series At your coop in Plushie Algorithms LLC, you are given a program and some notes from your mentor. You are tasked with nding out how many steps it takes for some functions in this program to nish processing a list of elements. i. One major function of the program named foo is accompanied by these notes: 0 foo takes in a list of integers and produces an integer. (Implementation irrelevant) c When given a list with 1 element, it takes 1 steps. 9 When given a list with 2 elements, it takes 8 steps. 0 When given a list with 3 elements, it takes 27 steps. 0 When given a list with 4 elements, it takes 64 steps. 0 When given a list with 5 elements, it takes 125 steps. According to the trend in these notes, given a list with n elements, how many steps will this function take? Show all of your work or explain your answer as your mentor will want to look it over. ii. The other major function of the program, bar, uses foo to complete its computation. The function bar is implemented as follows: 0 For 2' between 1 and n (inclusive): Create a new list first_i with the rst 7) elements of the list Give first_i to foo to produce a number,ans Add ans to a running total (takes 1 step) 0 Report the total as the nal answer Additionally, the notes mention the following about bar: 0 bar takes in a nonempty list of integers and produces a single integer. o \"The \"for\" thing repeats work. The \"for\" thing will create a new list, use 00 and add to the total \"11\" times. Each time, it uses an integer starting from 1 and ending at n in place of i. 0 Creating first_i takes i steps. 0 Adding ans to the total is 1 step. Given a list of n elements, how many steps will bar take to nish? Make sure your nal answer has no summation symbols (e.g. Z). Show all of your work and reasoning to your mentor. You will need the following equality as well Zia = n2(n+ 1)2