Kindly don't paste chatGPT answers.

I build an information source S by flipping a fair coin multiple times and recording the sequence of outcomes (c.g. THTHHH), subject to the following rule: I flip the coin 3 times, hoping to get three H's in a row. If I don't succeed, I repeat and flip again 3 times. I continue in this manner, and stop only if HHH is observed. If I don't get H HH after k flips, I give up and stop. In any case S records the entire sequence of flips. (a) Determine the entropy of S. (b) Determine how the entropy behaves as k -> co: either show that it's unbounded or compute its limit if one exists