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Chapter 7: Q. 63 (page 593)

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

2-k-110

Short Answer

Expert verified

The given sequence is monotonic and unbounded.

Step by step solution

01

Step 1. Given Information.

The given sequence is2-k-110.

02

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

To determine whether the sequences are monotonic or not, we will use the difference test.

Let the general term is ak=2-k-110.

So, the ak+1term is

ak+1=2-k+1-110.

According to the difference test,

ak+1-ak=2-k+1-110-2-k-110=2-k10-2+k-110=-k+k-110=-110

Since ak+1-ak<0.

Thus, the sequence is strictly decreasing and it is monotonic.

03

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

We have seen as the value of kincreases, akdecreases.

Thus, the sequence is unbounded.

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