Recall the definition of the Master Theorem and its three cases. Which case does the given recurrence relation fall under, and why?

To prove Case 1 of the Master Theorem, consider the recursion tree method. What is the height of the recursion tree, and how does the work done at each level contribute to the total work?

Use the geometric series sum formula to derive the total work done. Show that the sum converges to a constant factor of \( n^{\log_b a} \) when \( a > b^k \).