Q1

a. The number of operations executed by algorithms A and B is 8n log(n) and 2n² , respectively. Determine n₀ such that A is better than B for n n₀.

b. What is the sum of all the even numbers from 0 to 2n, for any integer n 1?

c. Show that (n + 1)5 is O(n 5 ).

d. Show that n is O(n log n).

e. Show that is O(n³).