Error solving the next recurrence: $T(n)=7T(n/2)+n^2$
Some of your sums have typos, but you already have the right answer.

Here's a useful fact about logarithms:

$a^{\lg b} = 2^{(\lg a) \cdot (\lg b)} = 2^{(\lg b) \cdot (\lg a)} = b^{\lg a}$

Apply it to your answer, keeping in mind that $\lg 7 \approx 2.8 &gt; 2$:

$O(7^{\lg n} + n^2) = O(n^{\lg 7} + n^2) = O(n^{\lg 7})$