n(n – 1) is O(n²). 2 Show that

n (a) Use Bernoulli's inequality to prove that (1 + /-/-) " > √n for all nЄ N.

Prove the following result below

Prove that n-1 3j(j-1) = n(n – 1)(n– 2). j=0

BC:5.4 Let x[n] represent the number of automo- biles produced by a factory on a given day, n. Let the inventory (total number of completed cars at the factory) at the end of day n be represented by q[n]. Each day the factory ships 5/6 of the previous day's inventory and holds the remaining 1/6 of the previ- ous day's inventory for one full day of driving tests. The cars being tested on day n are included in the inventory count for day n. The day after testing, all of the tested cars are shipped. Let y[n] represent the number of cars shipped on day n. Specify a flow di- agram and a difference equation (in standard form) that describe together the number of cars shipped as a function of number of cars produced and the history of the number of cars shipped.

|| || = 1 NN N/10 1+ + x+y 11 AN

How would I solve this problem? I'm so confused with this problem.