Alternating series, absolute and conditional
Alternating signs let $\sum \tfrac{(-1)^n}{n}$ converge where $\sum \tfrac1n$ cannot; three conditions are needed and the decreasing one is the one that gets skipped. Then a second question — what $\sum|a_n|$ does — splits convergence into absolute and conditional.
About 20 minutes7 activities Caderno em papel