Solving recursive function with floor The recursive function is this:
$$ T(n) = 
\begin{cases}
2 & \text{ for }n=1;\\
T \left( \lfloor \frac{n}{2} \rfloor \right) + 7 &,\text{ otherwise}
\end{cases}
$$
Based on the definition of the function, the right side becomes: 
$T(n) = T( \lfloor \frac{n}{2^i} \rfloor) + 7 * i;$
The procedure stops when $\lfloor \frac{n}{2^i} \rfloor == 1$
The problem is how do I continue it from there?

Your problem appears, for instance, in the analysis of binary search.  The master method is helpful to solve the recursion.
https://en.wikipedia.org/wiki/Master_theorem_(analysis_of_algorithms)
If
\begin{equation}
T(n) = T\left(\frac{n}{2}\right) + O(1)
\end{equation}
then
\begin{equation}
T(n) \in  O(\log n)
\end{equation}
 Apply Master theorem case $c = \log_b a$, where $a = 1, b = 2, c = 0, k = 0$
For more details, check
    http://www.math.dartmouth.edu/archive/m19w03/public_html/Section5-2.pdf
