How can we teach students the difference between sequences and series?

[Meden Agan]

Sequences and series are related concepts, but they differ extremely from one another. I believe that students in integral calculus often confuse them. Part of the problem is that:

1. Sequences are usually taught only briefly before moving on to series.
2. The definition of a series involves two related sequences (terms and partial sums).
3. Both have operations that take in a sequence and output a number (the limit or the sum).
4. Both have convergence tests for convergence (monotone convergence and squeeze theorem vs. root test, ratio test, etc.).

What methods can one use to teach students to distinguish between sequences and series? Specifically, strategies that address the above concerns. Answers are greatly appreciated if they include appropriate references.

 

[PeroK]

If a student struggles with this, then mathematics isn't for them. There are a lot harder concepts than this.

 

[berkeman]

What methods can one use to teach students to distinguish between sequences and series?

Um, recognizing the different punctuation?

 

[Steve4Physics]

What methods can one use to teach students to distinguish between sequences and series?

The difference between sequences and series is trivial. Are you sure you’ve asked what you intended?

But there could be casual misuse of terminology. Typically a student might use the word 'series' when they mean 'sequence'. (A bit like a physics student using 'velocity' when they mean 'speed'.)