(10 points) Recall that S(H) is the minimum number of nodes in a height-balanced tree of height H. Using induction to prove that S(H) = Fib(H+3) - 1 for all H 0 by induction. Hint: We observed in class that S(H) = S(H-1) + S(H-2) + 1. Use this observation in your proof. (If you missed this observation, you should review it, asking for help if needed, until you convince yourself this is true.) Here are a couple of supplementary online resources on induction that I like: (1) Video demo(https://www.youtube.com/watch?v=ruBnYcLzVlU) and web page (this page does a few examples, and explains more about why is works with a couple of cool examples showing what happens if you use math induction incorrectly!)