$(5$ points$)$ Solve the following recurrence using the Back Substitution method, and check

your results with the Master Theorem Show ALL your work including at least three sub$-$

stitutions before you move to $k$ steps, and computed summations. No credit will be given if

students don't show all their work in detail.

$T(n)=16T(\frac{n}{2})+n^3+n+1$