How can I give T(n) in asymptotic notation for recursions?

Question

I need to give T(n) in asymptotic notation for the following recursions:

T(n) = 2T(n/2) + *big_omega(n)
T(n) = T(n-1) + *big_omega(n)

And possibly explain the reasoning? Thanks

Answer 1

Use master theorem

1) n = O(n^log_n(n)) -> Case 1

Use unrolling

2) T(n) = T(n-1) + O(n)

T(n-1) = T(n-2) + O(n-1) -> T(n) = T(n-2) + O(n-1) + O(n)

...

try to form a form a non recursive formula