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Absolute convergence


A Serie é absolutely convergent if the module series

is convergent.

For example, the alternating series
is absolutely convergent as the series of modules is a p-series with p = 2> 1 and therefore convergent.

Theorem

If an infinite series is absolutely convergent, so the series is convergent.

D'Alembert test

Be a series of non-null terms and be . So:

* If L <1, the series is absolutely convergent.

* If L> 1, (including L = ), the series is divergent.

* If L = 1, the test fails (nothing can be said). Next: Series Summary