AP Calculus BC glossary
Alternating series error bound
For an alternating series that satisfies the alternating series test, the error in using a partial sum is less than the absolute value of the first omitted term. It is the simplest error bound in the course.
It works because the partial sums of an alternating series overshoot and undershoot the true sum in turn, so the sum is always trapped between consecutive partial sums.
The mistake
Using the last term you included rather than the first one you dropped. The bound is the size of the next term, the one not in your partial sum.
Appears in: Unit 10: Infinite Sequences and Series (BC)