key problem in C quarter of calc is dealing with notation,
esp. big sigma/summation notation.
I think you should take the bulls by the horns; make people work
-just- with the notation.
EG: prove that \Delta \Sum = \Id in 2 ways:
(firstly, always expand this out to
 \sum_{n=0}^N a_n - \sum_{n=0}^{N-1} a_n)
1: write out all the terms, cancel
2: write \sum_{n=0}^N a_n = a_n + \sum_{n=0}^{N-1} a_n
   and just cancel: this is exactly just making the above formal
[actually, start by really stupid basic stuff like:
 "prove that $n!/(n-1)! = n$ by writing $n!=n(n-1)!$"
 and: show that $(2n)! = n!!*2^n*n! (hint: odds and evens)]
Likewise:
- show that $(n^2-n)/2$ and $\sum_{k=0}^{n-1} k$ have the same
  difference, and agree at 0; hence conclude that they're equal