Solve Recurrence for $T(n) = 7T(n/7) + n$
Here is what I get:
\begin{align}
T(n) &amp;= n + 7T(n/7) \\ &amp;= n + 7(n/7) + 7^2 T(n/7^2) \\ &amp;= n + 7(n/7) + 7^2(n/7^2) + 7^3 T(n/7^3)
\end{align}
and so on. Each of the summands equals $n$, and there are $O(\log n)$ of them.