Consider the following recurrence:T$($n$)=3$T$($n$/3)+3$T$($n$/2)+$ n$^2$T$(1)=$ CWe will show that T$($n$)=$ O$($nlog$(13/3)).$ To do this, start by examining the first three levels of the recursion tree, showing how to compute the amount of work at each level. From here, establish a formula for the amount of work on level i$.$ Then, determine the last level of the recursion tree $($note that it is sufficient to focus on the largest piece at level i$,$ as we are only concerned with a Big$-$O bound$).$ Finally, construct a summation which totals the amount of work over all levels and show why this summation is T$($n$)=$ O$($nlog$(13/3))$