AP Calculus BC glossary
Sequence
A sequence is an ordered list of numbers indexed by the positive integers. It converges when its terms approach a single finite limit, and the tools for deciding that are limit techniques applied with n in place of x.
A sequence converges when its terms approach a single limit. A series converges when its partial sums approach a limit, which is a stronger and quite different requirement.
Because the index runs through integers only, a sequence limit can be evaluated by treating as a continuous variable and taking the limit at infinity, which is what licenses L'Hopital's rule on sequence limits.
The mistake
Concluding a series converges because its terms go to zero. Terms going to zero is necessary but nowhere near sufficient.
Appears in: Unit 10: Infinite Sequences and Series (BC)