The discussion revolves around evaluating the limit as k approaches infinity of the absolute value of the expression (cos(πk + π))/(cos(πk)). The subject area pertains to limits and trigonometric functions.
Participants are engaged in exploring the limit and its properties, with some expressing confusion and seeking clarification. There is a recognition of the alternating values of the cosine function, but no consensus has been reached on the limit itself.
Some participants mention having consulted various sources without finding satisfactory explanations, indicating a potential gap in understanding or available resources.
If k is an integer, what is cos(πk) ?Chaoticoli said: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.
Chaoticoli said: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.
Chaoticoli said:It must alternate between -1 and 1.