An alternating series CONVERTS if:

* Its generic term, in **module**, tends to **zero.**

* The series of **modules is decreasing.**

There are three different ways to verify that the module series is **decreasing.**

**The) **check that for all **"k"** positive integer, .

**B) **check that for all **"k"** positive integer, .

**ç) **consider the function** f (x) = f (n)** and check the signal of its derivative. If **f '(x) <0**, then** f** It is decreasing.