Q. 67 - Calculus

Question

Determine whether the sequences in Exercises 63–74 are monotonic or not. Also determine whether the given sequence is bounded or unbounded.

$\left\{1, -1, 1, -1, 1, ...\right\}$

Step-by-Step Solution

Answer

The given sequence is not a monotonic sequence but it is a bounded sequence.

Step 1. Given Information.

The given sequence is $\left\{1, -1, 1, -1, 1, ...\right\}.$

Step 2. Determine whether the sequences are monotonic or not.

As we can depict from the given sequence that it is neither increasing nor decreasing. Thus, the sequence is not a monotonic sequence.

Step 3. Determine whether the given sequence is bounded or unbounded.

The terms of the given sequence are either 1 or -1, thus the sequence is bounded by 1 and -1.