Problem Set 3

Finding the closed form for the given function was tricky. Unwinding it in the conventional sense didn’t quite lead to the closed form. The crucial steps towards finding the closed form were done after unwinding and recognizing the patter in the un-winded terms. After unwinding and simplifying, I realized that each term was a multiple of 3. More specifically, the ratio between two consecutive term is 3. Thus the expansion was that of a geometric series. Thus to find the closed from of G(n), I had to use the geometric series formula, and plug in the ratio and the first term in the series. After finding the closed form of G(n), proving it using simple induction was pretty straightforward.