I think you are trying to find an explicit formula for T by looking for a pattern.Is there any critique about each step?
Step 1: Write the recursive functionI think you are trying to find an explicit formula for T by looking for a pattern.
One comment is that I think you need to expand expressions like
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in order to see the correct pattern.
Another is that these are not equivalent:
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That probably won't be used in the correct solution, but you do need to learn to be careful with logs.
A thought about the problem itself: Have you considered what happens if n is not a power of 2? I started by calculating T(2), T(3), T(4), and this is instructive. Your final answer is likely to involve something like the greatest-integer function.
One specific question: Can you tell us what steps you were taught to take, so we can understand your approach?
You haven't expanded, as I use the term. In particular, your step 3 has an expanded form, which doesn't match your results from step 2.Step 2: Expand the recursive function three times
How is i defined?Step 3: Write the last T(n) in terms of i
What does this refer to? Will we understand when you state the problem fully?Find c and n when claiming the equation is Big O