# Unrolling study problems

### Problem 1

Find a closed form for the following recurrence using unrolling.
Show your work clearly, including at least three substitution
steps and a step that summarizes the result of the kth substitution
using summation notation.
You may assume that n is a power of 2 so that
the input to T is always an integer. You may wish to consult
a table of closed forms for common summations.

\(T(1) = 5 \)
\( T(n) = 3 T(n/2) + 7\) for \(n \ge 2\)

Stuck? See the hints.

When you have a calculation
that seems close to correct, look at the
solution.