I think you could probably show a smart group of first year calculus students how to get an exact formula for the Fibonnaci numbers using generating functions, which basically just boils down to knowing partial fraction decomposition and a few standard power series. You could then point them to Wilf's book if this makes them curious about generating functions in combinatorics.

I think you could probably show a smart group of first year calculus students how to get an exact formula for the Fibonacci numbers using generating functions, which basically just boils down to knowing partial fraction decomposition and a few standard power series. You could then point them to Wilf's book if this makes them curious about generating functions in combinatorics.