I need help understanding this problem. im a little rusty with my logaritms/math so i'd appreciate an explanation of each step.

T(n) = 2T ([n/2])+n, (4.19) which is similar to recurrences (4.3) and (4.4). We guess that the solution is T(n) = O(n lgn). The substitution method requires us to prove that T(n) 0. We start by assuming that this bound holds for all positive m <>