Absolute convergence proving that limit =1

1. Apr 10, 2013

Chaoticoli

1. The problem statement, all variables and given/known data
limit as k--> infinity ABS VALUE((cos(pi*k+pi))/(cos(k*pi)))

2. Relevant equations

3. 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.

2. Apr 10, 2013

SammyS

Staff Emeritus
If k is an integer, what is cos(πk) ?

3. Apr 11, 2013

Chaoticoli

It must alternate between -1 and 1.

4. Apr 11, 2013

LCKurtz

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

5. Apr 11, 2013

SammyS

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

6. Apr 11, 2013

Chaoticoli

I understand now. Thanks :)