For example, if {a0,a1,a2,a3,...a0,a1,a2,a3,...} is the sequence,
the first difference is {a1−a0,a2−a1,a3−a2,...a1−a0,a2−a1,a3−a2,...},
and the second difference is {(a2−a1)−(a1−a0),(a3−a2)−(a2−a1),...(a2−a1)−(a1−a0),(a3−a2)−(a2−a1),...}.
I think that using facts from up to Calculus, perhaps derivatives, should be enough. I find myself going in circles and don't know how to approach this.
