#### To determine

Whether the series is convergent or divergent and obtain the sum if the series is convergent.

#### Answer

The series is divergent.

#### Explanation

**Given:**

The series is ∑n=1∞arctann.

Here, an=arctann.

**Theorem used:** Series test for Divergence

If limn→∞an does not exist or limn→∞an≠0, then the series ∑n=1∞an is divergent.

**Calculation:**

Obtain the limit of the sequence (the value of the term an as *n* tends to infinity).

limn→∞an=limn→∞(arctann)=arctan(∞)=π2≈1.57

Thus, the limit of the sequence is limn→∞(arctann)=π2.

Since limn→∞(arctann)≠0 and by using the Theorem (Series test for Divergence), the series ∑n=1∞arctann is divergent.

Therefore, the series is divergent.