Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Q. 5 (page 591)

What is meant by the index of a term of a sequence?

Short Answer

Expert verified

Ans: a0=0,a1=−1,a2=2,a3=−3,…

The subscript of the terms of the sequence is {0,1,2,3,...}.

Hence, the index of the term of the sequence is {0,1,2,3,...}.

Step by step solution

01

Step1. Given Information.

given,

What is meant by the index of a term of a sequence?

02

Step2. The objective is to explain the index of terms of the sequence.

If akis the sequence, then the subscript k is the index of the sequence akwhere k is a positive integer.

Let be the sequence akdefined as (−1)kkk=0∞

The terms of the sequence can be found by substitutingk=0,1,2,...

03

Step 3. Therefore,

a0=0,a1=−1,a2=2,a3=−3,…

The subscript of the terms of the sequence islocalid="1649307016389" {0,1,2,3,...}.

Hence, the index of the term of the sequence is {0,1,2,3,...}.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

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.

∑k=1∞ 12k−3/4

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.

∑k=1∞ 1+kk2

Leila finds that there are more factors affecting the number of salmon that return to Redfish Lake than the dams: There are good years and bad years. These happen at random, but they are more or less cyclical, so she models the number of fish qkreturning each year as qk+1=(0.14(−1)k+0.36)(qk+h), where h is the number of fish whose spawn she releases from the hatchery annually.

(a) Show that the sustained number of fish returning in even-numbered years approach approximately qe=3h∑k=1∞0.11k.

(Hint: Make a new recurrence by using two steps of the one given.)

(b) Show that the sustained number of fish returning in odd-numbered years approaches approximately qo=6111h∑k=1∞0.11k.

(c) How should Leila choose h, the number of hatchery fish to breed in order to hold the minimum number of fish returning in each run near some constant P?

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

2.2131313...

For each series in Exercises 44–47, do each of the following:

(a) Use the integral test to show that the series converges.

(b) Use the 10th term in the sequence of partial sums to approximate the sum of the series.

(c) Use Theorem 7.31 to find a bound on the tenth remainder, R10.

(d) Use your answers from parts (b) and (c) to find an interval containing the sum of the series.

(e) Find the smallest value of n so that localid="1649224052075" Rn≤10-6.

∑k=0∞e-k
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free