AP Calculus BC glossary
Partial sum
The nth partial sum of a series is the total of its first n terms. The series converges precisely when this sequence of partial sums approaches a finite limit, which is what makes an infinite sum meaningful.
Partial sums turn an infinite question into a sequence question. For a geometric series they have a closed form, which is how the geometric sum formula is derived.
For an alternating series the partial sums bracket the true sum, jumping above and below it. That is exactly why the alternating series error bound is so simple.
Appears in: Unit 10: Infinite Sequences and Series (BC)