Sequences and series are related concepts but differ extremely from one another. I feel that students in integral calculus frequently mix them up. Part of the problem is that:
- Sequences are usually taught only briefly before moving onto series.
- The definition of a series involves two related sequences (terms and partial sums).
- Both have operations that take in a sequence and output a number (the limit or the sum)
- Both have convergence tests for convergence (monotone convergence and squeeze theorem vs. root test, ratio test, etc.)
What methods can I use to teach students to distinguish between sequences and series? Specifically, methods that adress the above concerns.