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In Exercises 4–11, give examples of sequences satisfying the given conditions or explain why such an example cannot exist.
Two divergent sequences {ak}and {bk}such that the sequence {akbk}diverges.

Short Answer

Expert verified

The example of the sequence is {ak}={k2}and {bk}=k.

Step by step solution

01

Step 1. Given Information.

Two divergent sequence {ak}and{bk}.

02

Step 2. Consider the divergent sequence.

Consider the sequence {ak}={k2}which is strictly increasing and not bounded above.

So it is divergent sequence.

Consider the sequence {bk}={k}which is strictly increasing and not bounded above.

So it is divergent sequence.

03

Step 3. Division of the sequence.

The sequence {akbk}={k}which is a decreasing sequence and not bounded above.

And the sequence does not converge to zero.

So the division of two divergent sequence can be divergent.

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