# Is it an Alternating Series?

• remaan
In summary, the conversation discusses whether a given series is alternating or not and how to test for convergence or divergence using the root test. The conversation also clarifies that the given series is not alternating and provides a correction regarding the value of 1/arctan(n)^n.

## Homework Statement

Is this an alternating series : (-1)^n / ( arctan n ) ^ (n)

## Homework Equations

I know that the alternating series should have (-1) to any power, but also the signs should be - , + , - , + ... or the opposit,

## The Attempt at a Solution

I am ok with this I know that for testing Con. Or Div. of this we should use the root test

But this series. But the problem is " Is this seris alternating or not"

Becasue if not it will be treated normally with a root test and it will Con.

For me I think that it is not "Alternating "

What do you think ?

Does 1/arctan(n)^n decrease to zero? That's what they want to you check.

mmm, do you mean the limit, if so no. It goes to inifity.

So, this is NOT an alternating sries, right ?

No. 1/arctan(n)^n doesn't go to infinity. Tell me why you think it does.

ohhh, Ya , I remembred it goes to Pie/ 2
Right ?

arctan(n) goes to pi/2. 1/arctan(n)^n doesn't.

## 1. What is an alternating series?

An alternating series is a mathematical series where the signs of the terms alternate between positive and negative. This means that each term in the series is either positive or negative, and the sign changes with each term.

## 2. How do you determine if a series is alternating?

A series can be determined to be alternating by checking if the signs of the terms alternate between positive and negative. If the signs do not alternate, then the series is not alternating.

## 3. What is the alternating series test?

The alternating series test is a mathematical test used to determine if an alternating series converges or diverges. It states that if the terms of an alternating series decrease in absolute value and approach 0, then the series will converge.

## 4. Can an alternating series diverge?

Yes, an alternating series can diverge if the terms do not decrease in absolute value and approach 0. This means that the series does not follow the conditions of the alternating series test and can potentially have no limit.

## 5. How is the convergence of an alternating series calculated?

The convergence of an alternating series is calculated by using the alternating series test. This involves checking if the terms decrease in absolute value and approach 0. If these conditions are met, then the series will converge and the limit can be calculated.