Sum of Geometric Series with cosine?

[dan38]

Homework Statement

With a series like:
pi^(n/2)*cos(n*pi)

How am I meant to approach this?
Do I use the Squeeze Theorem?

Homework Equations

The Attempt at a Solution

 

[Infinitum]

I believe you are trying to find the sum as n->infinity?

If so, you should start by checking whether the series converges or diverges.

 

[oli4]

Hi dan38
As Infinitum suggested, you probably are looking for convergence/divergence of the serie
I suppose you are being confused by the cos 'trick'.
But look at is closely.. what possible values do you have for cos(n∏) ?
1, -1, 1, -1, ... that is, (-1)^n
Are you familiar with D'Alembert's rule to decide on convergence ?

Cheers...

 

[dan38]

ah I see
so then it would become

(pi)^0.5 * (pi)^n * (-1)^n

pi^0.5 * ( - pi )^n

-pi^1.5 * ( - pi )^(n-1)

Of the form required
where a = -pi^1.5 and r = -pi

since r > 1
then it is divergent?

 

[oli4]

Well you're notation is confusing, you are supposed to use absolute values and somehow you get to -∏,
but yes, you would get to ∏>1 and therefore it diverges

Cheers...