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Chapter 7: Q. 17 (page 592)

Give an example of a sequence with neither an upper bound nor a lower bound.

Short Answer

Expert verified

Ans: The sequence (鈭�1)kkk=0鈭�neither has an upper bound nor a lower bound.

Step by step solution

01

Step 1. Given information.

Give an example of a sequence with neither an upper bound nor a lower bound.

02

Step 2. The objective is to give an example of the sequence which has neither an upper bound nor a lower bound.

Consider the sequence (鈭�1)kkk=0鈭�

Find the terms of the sequence by substituting k=0,1,2,3,....

The terms of the sequence are(鈭�1)0鈰�0,(鈭�1)1鈰�1,(鈭�1)2鈰�2,(鈭�1)3鈰�3,(鈭�1)4鈰�4,鈥�鈰�

Hence, the terms of the sequence arerole="math" localid="1649305772298" {0,-1,2,-3,4,...}.

03

Step 3. Thus,

The above sequence is neither an increasing sequence nor a decreasing sequence.

Hence, the sequence neither has an upper bound nor a lower bound.

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