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Chapter 7: Q. 7 (page 603)

In Exercises 4鈥�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 {ak.bk}diverges.

Short Answer

Expert verified

The examples of such divergent sequence is {ak}={k} and {bk}={k}.

Step by step solution

01

Step 1. Given Information.

Two divergent sequences {ak}and {bk}such that the sequence {ak.bk} is divergent.

02

Step 2. Consider the sequence.

Consider the sequence,

{ak}={k}{bk}={k}

Both are monotonically increasing function and are not bounded above.

So the sequences are divergent.

03

Step 3. Explanation of the statement.

The product of the sequence {ak.bk}={k2}is again a strictly increasing sequence and not bounded above.

So the resultant sequence is also divergent.

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Most popular questions from this chapter

Explain why the integral test may be used to analyze the given series and then use the test to determine whether the series converges or diverges.

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