# How do you determine if the series the converges conditionally, absolutely or diverges given #sum_(n=1)^oo (-1)^(n+1)arctan(n)#?

##### 1 Answer

Apr 13, 2018

The series diverges.

#### Explanation:

For

**The Alternating Series Test**

An alternating series

- All the
#a_n# terms are positive (the sign of each term in the series alternates) - The terms are eventually weakly decreasing (
#a_n>=a_(n+1)# for large enough#n# ) #a_n->0#

The series fulfils the first condition of the test but fails the second condition (and third) as

And if the series doesn't converge conditionally then it doesn't converge absolutely.