1. A mathematical sequence that does not converge to a finite limit; a sequence whose terms do not approach a specific value as the number of terms increases indefinitely
The sequence 1, 2, 3, 4, 5... is a divergent sequence because it increases without bound.
A sequência 1, 2, 3, 4, 5... é uma sequência divergente porque aumenta sem limite.
2. In calculus and analysis, a sequence where the limit does not exist or is infinite
We proved that the harmonic series forms a divergent sequence when considering its partial sums.
Provamos que a série harmônica forma uma sequência divergente quando consideramos suas somas parciais.
This is specialized mathematical terminology used in university-level mathematics courses in both Brazil and the USA. The concept is fundamental to calculus and real analysis. Both countries use virtually identical definitions and notation in their mathematics education systems.