T(n)=T(n1)+logn. T(2)=1

a) Draw a recursion tree for T(n). Identify its depth and the sum of non-recursive terms (per level), for each level. Exaggerate and simplify to get an upper bound for T(n), and then underestimate and simplify to get a matching lower bound. (Always using Theta notation). Your bound should be in a form that is easily recognizable, and easy to compare to simple functions like linear, quadratic, etc.

(b) Derive the same upper bound for T(n) that you got in (a), by induction.