This morning, for a little first day of school fun, we played with Grandi’s Series.
I’ve seen the series pop up in a few places in the last few days – first in part of a little note I wrote up inspired by a Gary Rubenstein talk:
A Talk I’d live to give to calculus students
and then a day or two later in this tweet from (the twitter account formerly known as) Five Triangles:
So, what’s going on with this series? What would the boys think?
Here’s their initial reaction:
And here’s their reaction when I showed them what happens when we assume that the series does sum to some value x:
We have touched a little bit on this series (and my favorite math term “Algebraic Intimidation”) previously:
Jordan Ellenberg’s “Algebraic Intimidation”
It is fun to hear the boys struggle to try to explain / reconcile the strange ideas in Grandi’s series. I’m also glad that they are learning to think through what’s going on rather than just believing the algebra.