Determine whether the sequence $\{ \cos ( k \pi ) \}$ is monotonic or eventually monotonic and whether the sequence is bounded. If the sequence is convergent, find the limit.
A) Monotonic, bounded, converges to 1
B) Monotonic, unbounded, diverges
C) Not monotonic, bounded, diverges
D) Monotonic, bounded, converges to 0

Question

Quizplus · Accepted Answer

The sequence $\{ \cos ( k \pi ) \}$ alternates between 1 and -1 for integer values of $k$, making it not monotonic. However, it is bounded between -1 and 1. The sequence does not converge because it does not approach a single value.

Determine Whether the Sequence {cos⁡(kπ)}\{ \cos ( k \pi ) \}{cos(kπ)}

Determine Whether the Sequence $\{ \cos ( k \pi ) \}$