Some quick thoughts on Test #1: 3 questions, 8 marks each. The first one was a binomial expression which I attempted to solve via simple induction. I'm fairly sure this is the right flavour to use for this question; except I got stuck on the induction step and couldn't figure out how to show P(n) --> P(n+1). I probably spent a little too much time on this question.
Question 2, with the Fibonacci sequence. I used complete induction. I don't totally remember the question. In my head I think i'm getting it confused with #1 and mixing the problems. I think it was F(n)^2 > 2n? Or something of that nature. Using complete induction, my proof went something like this; I showed the F(n) is the sum of F(n-1) and F(n-2) [by definition], which are both greater than 2(n-1) and 2(n-2) respectively [by IH]. Since F(n)'s predecors were both greater than 2n it should follow F(n) also.
Question 3, I'm drawing a blank on what the question was. I do remember running out of time since I spent a little much time thinking about #1's induction step. I think I started out using simple induction and then realized I should've used complete induction. I ran out of time to fix this and to finish the proof, but I had a structure of a proof and I put down some ideas of how to solve it.
Overall I felt prepared for the test, I just ran into a the problem of not being able to see the induction step for #1 which cost me some time. I always feel a little rushed when writting a 50min test. But I can't complain, everyone else is in the same boat and a few people seemed to have finished and left the room with some time to spare.
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2 comments:
We should have the graded tests back this week, so there's probably nothing to worry about.
Ya the markings been pretty quick considering the size of the class and number of tests, assignments and problem sets.
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