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Vito Prosciutto: Teaching community college math on the road to a PhD.

Tuesday, April 20, 2004

21:35
Observations 

Not a whole lot to report. I sat in on a teacher's classes who I'd not seen before and got my first glimpse of the precalc class. They were doing infinite series which is a topic that I'm always interested to observe being taught because I managed to more or less miss it in my own formal math education (I took an AB Calc class, but the BC test so I managed to miss that whole portion of Calculus where it's traditionally taught). I ended up catching a slight error in the teacher's instruction where she claimed that
nn/(n+1)n
would approach 1 as n approached infinity. My instinct was that it would have to decrease since we were taking progressively larger exponents of the fraction n/(n+1) which would be less than 1. My first guess was that it might tend towards 0, but I later realized that it would actually tend towards 1/e. I thought of a better argument that it was in fact 1/e then the calculator appeal I was able to use in class when I thought about inverting the fraction and with a bit of algebra I got (1+1/n)n whose limit as n approaches infinity is in fact e (the advanced algebra text we use, in fact defines e that way).

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