# Unrolling Problem 1

Here is the recursive definition, for reference

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

### Partial Solution

First, substitute the recursive part of the definition into itself and
guess the pattern to get the result after k substitutions.

\(
\begin{eqnarray*}
T(n) &=& 3\cdot T(n/2) + 7 \\
&=& 3(3\cdot T(n/4) + 7) + 7 \\
&=& 3(3(3\cdot T(n/8) + 7) + 7) + 7
\end{eqnarray*}
\)

### Comments

Find and fix any errors in the above, then return to the hints page for
help with the rest of the calculation.