log() i=1 Problem 1. (1+1 points each for (a)-(6), 3 points for (g)) Consider the following summations that are functions of n: (a) f(n) = 3(5+3) T(c) fs(n) = (5) T(e) f(n) = (100 21) 1(f) fo(n) = (b) f(n) = (n + 2) L (d) f(n) = (2i log(n) + log(n)) I(g) Arrange the functions in order of growth, from slowest growth on the left to fastest growth on the right. In the event of a tie, put the function with the smaller constant/terms to the left. No justification required. These are various quantities that will naturally come up throughout the semester in our analysis of varying data structures. You should use base 2 for each log and may assume that n is a power of 2. For each function f1 through fe above. compute the closed form for the summation (a formula that is directly in terms of n) and provide a tight Big-O bound for the formula (i... Big-e). To compute the closed form of each summation, you must show all work as a step-by-step derivation using the rules below and how you applied the rules). You may only use the following rules: RI. (cf0) = FC) = c56) . RO. 5(0) = S()+...+560 1)+ (S). 50+ for j O exists). Note: c is any constant relative to i, j, k , and the sum is always ( if k is smaller than the starting index. For example, to properly derive the runtime for BubbleSort from lecture "E" 0(1) = 0m2) you would need the following work: i=0 j=0 n-2 n-2 i (1) i=0 j=0 {(i 0 + 1)0(1)) by applying R3 with j = 0, k = i, and c = 0(1). i=0 n-2 ((i+1)O(1)) by arithmetic. i=0