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