Algorithms Question

WE NEED TO SHOW THAT THERE EXISTS POSITIVE CONSTANTS FOR C & n0 in our answers

Each step should state after it n >= n0 where n0 needs to be known eg 1 etc...

Answer question fully for thumbs up.

Question 1 By using the definition of Big-O, show that (a) n! + 3nisO(n!) A hint: prove an auxiliary inequality first and then use it for proving the main result. Below are two examples of auxiliary inequalities: or 3" s n! for n27. (b) 2n+4+4n is 0(4n) (c) 8n3n-2n + is O(n2) (d) n ++5+5+..-+ ,L s0(n), where n=2q, so that the last term is-1. 29-1 . 2q Hint: you can use the formula known for geometric series, without proving it