diverging series
[dɪˈvɜːrdʒɪŋ ˈsɪriz]
nounpl: diverging series
série divergente
1. In mathematics, an infinite series whose partial sums do not approach a finite limit; a series that does not converge
The harmonic series is a classic example of a diverging series because its partial sums increase without bound.
A série harmônica é um exemplo clássico de série divergente porque suas somas parciais aumentam sem limite.
2. A sequence of numbers added together where the sum tends toward infinity or oscillates indefinitely
When testing whether a series diverges or converges, mathematicians use various convergence tests like the divergence test.
Ao testar se uma série diverge ou converge, matemáticos usam vários testes de convergência como o teste de divergência.
This is specialized mathematical terminology used uniformly across English-speaking and Portuguese-speaking academic communities. It appears in calculus and analysis courses worldwide. The concept is fundamental to understanding mathematical analysis and is taught identically in Brazil, Portugal, and the USA, making it a truly universal academic term.
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