The uniform and pointwise types of this property may be contrasted for sequences, and Cauchy sequences in a complete space always have this property. A limit approaching zero is necessary but not sufficient for this property, which exists when the root test gives a value less than one or the integral test gives a finite number. The harmonic se- ries lacks this property, but the alternating version thereof as well as p-series for p greater than one do have this prop- erty
The uniform and pointwise types of this property may be contrasted for sequences, and Cauchy sequences in a complete space always have this property. A limit approaching zero is necessary but not sufficient for this property, which exists when the root test gives a value less than one or the integral test gives a finite number. The harmonic se- ries lacks this property, but the alternating version thereof as well as p-series for p greater than one do have this prop- erty. This term also applies to geometric series with ratio between negative one and one. Give this term that describes series whose sum approaches a finite number, contrasted with divergence.
The uniform and pointwise types of this property may be contrasted for sequences, and Cauchy sequences in a complete space always have this property.
{convergence} [accept word forms]