Absolute convergence proving that limit =1

[Chaoticoli]

Homework Statement

limit as k--> infinity ABS VALUE((cos(pi*k+pi))/(cos(k*pi)))

Homework Equations

The Attempt at a Solution

Can someone prove to me why this limit is equal to 1? I have tried several other sources and I have not had any luck.

 

[SammyS]

Homework Statement

limit as k--> infinity ABS VALUE((cos(pi*k+pi))/(cos(k*pi)))

Homework Equations

The Attempt at a Solution

Can someone prove to me why this limit is equal to 1? I have tried several other sources and I have not had any luck.

If k is an integer, what is cos(πk) ?

 

[Chaoticoli]

It must alternate between -1 and 1.

 

[LCKurtz]

Homework Statement

limit as k--> infinity ABS VALUE((cos(pi*k+pi))/(cos(k*pi)))

I have tried several other sources and I have not had any luck.

Tried other sources? Have you tried working it yourself? What have you done so far?

 

[SammyS]

It must alternate between -1 and 1.

What is \displaystyle\ \left|\frac{\pm1}{\pm1}\right|\ ?

 

[Chaoticoli]

I understand now. Thanks :)