Teach 180: My Geeky Lightbulb Moment (Day 163)

In PreCalculus today, we were doing some problems involving summation.  One was the sum of n²  from n = 1 to 4.  I knew Desmos could do this one and I showed my students how this worked in Desmos.

Then, we did the following "by hand".

I asked my students, "what would Desomos do with this problem".  I wasn't really sure.  When I entered the expression, it didn't give me "an answer", it gave me a graph.  "Why is it doing that?" I wondered.

And then it dawned on me!  Desmos was graphing the polynomial that resulted from the summation.  We confirmed this as a class by entering the expression 1 + x + x²/2 + x³/6 + x⁴/24 in line 2 and it graphed over the graph that was already there.  As I was thinking aloud and having my lightbulb moment, my students asked me, "Wait, you mean you haven't done this in Desmos before?"  They thought I was acting surprised and had done this before.  I do that sometimes.  But not this time, my surprise was real.  About an hour later, I shared my discovery with the colleagues in my math department.  They were also impressed.  This is definitely something that can't happen on a TI-whatever.