Question $2)$ Compute the following recursive running times using the "Guess and Inductive

Reasoning" method:

$2-1)T(n)=3T(\frac{n}{2})+n,$ for this item, please start with this initial guess: $T(n)=O(n)$ and update your

guess if it does not work.

$2-2)T(n)=3T(\frac{n}{2})+n^2,$ for this item, please start with this initial guess: $T(n)=O(n)$ and update your

guess if it does not work.

$2-3)T(n)=T(n-1)+5$

$2-4)T(n)=2T(n-1)+7,$ Hint: $T(n)=O(2^n-1)$ can be a good guess