At the end of class I started an application of the binomial theorem, with the the aim of obtinaing a series expenasion for 'e'. I realized this is actually more complcated than I planned. You can read about it here
What I wanted to show in class was equation (4) with x=1. That is
e = 1 + 1/2! + 1/3! + 1/4! + ...
There are many wrong proofs of this on the internet.
I will expain what the basic difficulty is in class next time.