Final answer:
The limit of cos²(n) as n approaches infinity does not exist because cos²(n) oscillates between 0 and 1 as n increases without approaching a single value.
Step-by-step explanation:
The question asks to determine the limit of cos²(n) as n approaches infinity. Given the periodic nature of the cosine function, it oscillates between -1 and 1. As n becomes very large, the values of cos²(n) continue to oscillate and do not approach a single limit. Therefore, the limit of cos²(n) as n goes to infinity does not exist since it does not settle towards a specific value.
To determine the limit as n tends to infinity of cos²(n), we can use the fact that the cosine function oscillates between -1 and 1. Since we are taking the square of the cosine function, the result will always be between 0 and 1. Therefore, the limit as n approaches infinity of cos²(n) is 1.