Is the Series Alternating: (-1)^n / (arctan n)^n?

[remaan]

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 ?

 

[Dick]

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

 

[remaan]

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

 

[remaan]

So, this is NOT an alternating sries, right ?

 

[Dick]

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

 

[remaan]

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

 

[Dick]

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