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Chapter 7: Q. 3 (page 591)

What is a sequence?

Short Answer

Expert verified

Asequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Step by step solution

01

Step1. Given Information

Consider the term "sequence".

The objective is to explain the sequence.

The sequence is a function from the set of positive integers to the real numbers.

02

Step2. Explanation

Consider the following sequence from the set of positive integers to the real numbers.

It is written asa:Z+鈫�R, whereZ+is the set of real numbers andRis the set of real numbers.

03

Step3. Explanation

the Notation of the sequence is as shown below

The sequence is denoted byakwherekis the index and is a positive integer.

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Most popular questions from this chapter

Determine whether the series 803-203+53-512+鈥�converges or diverges. Give the sum of the convergent series.

Use any convergence test from this section or the previous section to determine whether the series in Exercises 31鈥�48 converge or diverge. Explain how the series meets the hypotheses of the test you select.

鈭�k=1鈭�kk2+3

Prove Theorem 7.24 (a). That is, show that if c is a real number and鈭�k=1鈭�ak is a convergent series, then 鈭�k=1鈭�cak=c鈭�k=1鈭�ak.

Express each of the repeating decimals in Exercises 71鈥�78 as a geometric series and as the quotient of two integers reduced to lowest terms.

0.237237237...

Use either the divergence test or the integral test to determine whether the series in Exercises 32鈥�43 converge or diverge. Explain why the series meets the hypotheses of the test you select.

35.鈭�k=1鈭�k2+k2
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