I did a lot of scratch work for problem set 3, and unwound G(n) a number of different ways before finally determining a satisfactory closed form. I was (happily) surprised to see that Danny's hint on the forums correlated to this form - in fact, I think I was able to determine it without keeping the constant terms separate, perhaps by luck or maybe a good eye. Nonetheless, I found this problem set to be manageable, while still being interesting and challenging enough to find some level of "fun" in it.
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I had started out thinking that everybody would find the sum of a geometric series very familiar (from calculus), but then I relented and decided that it was fair to remind them.
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