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Chapter 7: Q. 67 (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.

1,-1,1,-1,1,...

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 is1,-1,1,-1,1,....

02

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

As we can depict from the given sequence that it is neither increasing nor decreasing. Thus, the sequence is not a monotonic sequence.

03

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

The terms of the given sequence are either 1or-1,thus the sequence is bounded by1 and -1.

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Most popular questions from this chapter

In Exercises 48鈥�51 find all values of p so that the series converges.

鈭�k=2鈭�1klnkp

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.

鈭�k=1鈭�鈥�kek

Iflimk鈫�鈭�akbk=鈭�and鈭�k=1鈭�_____Convergesthen鈭�k=1鈭�_____(converges/diverges).

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.

鈭�k=3鈭�鈥�1(k鈭�2)2

Use either the divergence test or the integral test to determine whether the series in Given Exercises converge or diverge. Explain why the series meets the hypotheses of the test you select.

鈭�k=1鈭�鈥�k鈭�3/2
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