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Chapter 7: Q. 4 (page 591)

What is a term of a sequence?

Short Answer

Expert verified

Each number in the sequence is called a term.

Step by step solution

01

Step1. Given Information

Consider the sequence.

The objective is to explain the term of sequence.

If k is the index of the sequence {ak}where k is a positive integer, the outputak is the term of the sequence.

02

Step2. Explanation

Let akbe the sequence defined as (鈭�1)kkk=0鈭�.

The term of the sequence can be found by substituting k=0,1,2,..

03

Sep3. Given Information

Therefore, a0=0,a1=鈭�1,a2=2,a3=鈭�3,鈥�

Hence, the terms of the sequence are{0,鈭�1,2,鈭�3,鈥�}.

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Most popular questions from this chapter

Use the divergence test to analyze the given series. Each answer should either be the series diverges or the divergence test fails, along with the reason for your answer.

鈭�k=1鈭�鈥�1kk

Use the divergence test to analyze the given series. Each answer should either be the series diverges or the divergence test fails, along with the reason for your answer.

鈭�k=1鈭�k3k+100

Use the divergence test to analyze the given series. Each answer should either be the series diverges or the divergence test fails, along with the reason for your answer.

鈭�k=1鈭�1k

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=0鈭�鈥�e鈭�k鈭�k=0鈭�鈥�e鈭�k

For a convergent series satisfying the conditions of the integral test, why is every remainder Rnpositive? How can Rnbe used along with the term Sn from the sequence of partial sums to understand the quality of the approximation Sn?
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