1. Prove that Vk € N, 1k + 2k + . . . +nk € ©(nk+1). 2. Suppose that the functions f1, f2, 91, 92 : N → R≥0 are such that f₁ = O(91) and ƒ2 Є ☹(92). Prove that (f1 + ƒ2) € ☹(max{91,92}). Here (f1 + f2)(n) = f1(n) + f2(n) and max{91, 92}(n) = max{91(n), 92(n)}. 3. Let n Є N\{0}. Describe the largest set of values n for which you think 2″ < n!. Use induction to prove that your description is correct. Here m! stands for m factorial, the product of first m positive integers. 4. Prove that log2 n! € O(n log n).

hello im new, i only get 3 free questions and im failing i wish there was a way to grade up but there isn't so please help me with what you can i beg you,.

I need help with just part c. Someone on here already answered it for me but I'm really confused as there are steps missing and I'm not sure what to put in the calculator.  " The first quartile separates the lowest 25% of the observations from the higher 75% of the observations. The first quartile is denoted by Q1. The second quartile separates the lower 50% of the observations from the higher 50% of the observations. The second quartile is denoted by Q2.The second quartile is same as median. The third quartile separates the lowest 75% of the observations from the higher 25% of the observations. The third quartile is denoted by Q3. The third quartile can obtained as follows...." Third Quartile is 1 somehow, and I don't understand how it is.

Please answer math question number 4.  **Fill in all blanks** This is a practice question for my son so it is not taken for acadamic purposes.   Please only type the answer out, this will ensure a thumbed up answer. Other answer that are otherwise written in purpose will be given the opposite (thumbs down)