$(0\mathrm{.}5)$ Given the complexity function:

$T(n)=9T(\frac{n}{2})+n+1$

After applied the back substitution process, and after $k$ steps, $($note that some steps are

missing$),$ we have arrived to the expression:

$T(n)=9^{k}T(\frac{n}{2^k})+(n+1)+(\frac{9n}{2}+9)+(\frac{81n}{4}+81)+$dots

Compute the solution for the above expresion as a function of $n.$ Show all your work including

step by step the way you set up and solve your summations to get credit.