Problem

State whether the sequence, whose $n$th terms are indicated, is bounded and whether it is eventually monotone, increasing, or decreasing. (Select all that apply.) $\cos \left(n^{2}\right)$
bounded
not bounded
monotone
not monotone
increasing
decreasing

Answer

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Answer

The sequence $\cos \left(n^{2}\right)$ is \(\boxed{\text{bounded}}\) and \(\boxed{\text{not monotone}}\). It is neither increasing nor decreasing.

Steps

Step 1 ：State whether the sequence, whose $n$th terms are indicated, is bounded and whether it is eventually monotone, increasing, or decreasing. (Select all that apply.) $\cos \left(n^{2}\right)$

Step 2 ：The sequence $\cos \left(n^{2}\right)$ is \(\boxed{\text{bounded}}\) and \(\boxed{\text{not monotone}}\). It is neither increasing nor decreasing.

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