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Chapter 7: Q. 70 (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.

cos2蟺kk

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given Information. 

The given sequence iscos2蟺kk.

02

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

The given sequence is not a monotonic sequence because the sign of cos2蟺办k differs as kincreases.

03

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

The given sequence is bounded because-1鈮�cos2蟺办鈮�1,-1k鈮�cos2蟺办k鈮�1k.

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