Here is a list of past posts on the topics of sequences and series that I hope you find interesting and useful. The first two are suitable for precalculus students.
The first uses sequences and series for a very practical aim that affects almost everyone sometime in their life: paying off a loan. The next gives a good, and I hope, understandable explanation of what an irrational number is.
Amortization. When you have a mortgage on your home or your car, you make the same payment every month. Part of the money pays the interest on the outstanding balance for the last month; the rest pays down the principal so there is less to pay interest on next month. How payment computed?
A Lesson on Sequences. What is the square root of two? Really, what is it? This post is an outline of a lesson finding a sequence of numbers that converges to a specific number known in advance and by doing so defines that number.
The next three posts deal with convergences tests and are of interest to BC students at this time of year.
Reference Chart. An outline of the various convergence tests, and their hypotheses (when you can use them).
These two posts answer the question in their titles:
Which Convergence Test Should I Use? Part 1: Pretty much anyone you want!
Which Convergence Test Should I Use? Part 2: Specific hints and a discussion of the usefulness of absolute convergence