Login Registrieren

Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

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 ${a_{k}}$ where k is a positive integer, the output $a_{k}$ is the term of the sequence.

02

Step2. Explanation

Let $a_{k}$ be the sequence defined as ${\{(- 1)^{k} k\}}_{k = 0}^{\infty} .$

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

03

Sep3. Given Information

Therefore, $a_{0} = 0, a_{1} = - 1, a_{2} = 2, a_{3} = - 3, \dots$

Hence, the terms of the sequence are ${0, - 1, 2, - 3, \dots}$ .

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

Determine whether the series $\sum_{k = 0}^{\infty} e {(\frac{π}{3})}^{k}$ converges or diverges. Give the sum of the convergent series.

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.

$0.237237237 . . .$

Let $a : [1, \infty) \to ℝ$ be a continuous, positive, and decreasing function. Complete the proof of the integral test (Theorem 7.28) by showing that if the improper integral $\int_{1}^{\infty} a (x) d x$ converges, then the series localid="1649180069308" $\sum_{k = 1}^{\infty} a (k)$ does too.

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 $q_{k}$ returning each year as $q_{k + 1} = (0.14 {(- 1)}^{k} + 0.36) (q_{k} + h)$ , 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 $q_{e} = 3 h \sum_{k = 1}^{\infty} 0 . 11^{k} .$

(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 $q_{o} = \frac{61}{11} h \sum_{k = 1}^{\infty} 0 . 11^{k} .$

(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?

Prove Theorem 7.24 (a). That is, show that if c is a real number and $\sum_{k = 1}^{\infty} a_{k}$ is a convergent series, then $\sum_{k = 1}^{\infty} c a_{k} = c \sum_{k = 1}^{\infty} a_{k}$ .

See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

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