This question pertains to the recurrence equation T(n) = 125T(n/5) + 5n with base case T(1) = 1.

[a] Use the Master Theorem to predict the complexity class of the solution.

[b] Derive a closed-form formula for the recurrence. Identify each technique used in the process.

[c] Test the original recurrence against your closed-form formula for the case n=5 to see if they match.