Problem Set 3

One thing I noticed with CSC236 is that you cannot sit down and try and get the answer in a couple of hours... I was actually confused by the notion of a closed form. I wondered how to use repeated substitution, I thought hard about it but couldn't get a hint. Then I said to myself, "lets take a break!"

So I played a bit of unreal tournament 3 online with my friends while a small part of my brain was concentrating on the problem set. Suddenly out of the blue, I shouted "AHA!". All of a sudden, at random, a clue came to my head. I immediately exited the game and went back to the problem set.

After playing around with the numbers and continuosly re substituting onto itself, I came up with a sequence which could be easily written with summation symbols etc. The sequence was :

3^3 + 3^2 + 3^1 + ... I played around with the summation and found that it actually converged to P(n+1). That was the clue! After re arranging and some factorisation, I spent about half an hour trial-and-error and found the final equation that would be a closed form for the problem!

Then I said to myself, frequent breaks are really useful! Random hints might fall in when the brain is not fully concentrating on the subject. The human brain surprises us all the time...