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

Dominance Relationships for Sequences: Order the following sequences by dominance when a>0andb>1

k!

Short Answer

Expert verified

The required order of dominance sequence islnk<<ka<<bk<<k!

Step by step solution

01

Step 1. Given information

The given expression isk!

02

Step 2. Explanation

Use the concept of dominance relationships for simple sequences,

For any real number a>0andb>1, the following string of dominance holds.

lnk<<ka<<bk<<k! for k sufficiently large.

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.

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

Let a:[1,โˆž)โ†’โ„be a continuous, positive, and decreasing function. Complete the proof of the integral test (Theorem 7.28) by showing that if the improper integral โˆซ1โˆža(x)dxconverges, then the series localid="1649180069308" โˆ‘k=1โˆža(k)does too.

Explain why a function a(x) has to be continuous in order for us to use the integral test to analyze a series โˆ‘k=1โˆžakfor convergence.

Prove Theorem 7.24 (a). That is, show that if c is a real number andโˆ‘k=1โˆžak is a convergent series, then โˆ‘k=1โˆžcak=cโˆ‘k=1โˆžak.

Given thata0=-3,a1=5,a2=-4,a3=2andโˆ‘akk=2โˆž=7, find the value ofrole="math" localid="1648828803227" โˆ‘akk=3โˆž.

Leila, in her capacity as a population biologist in Idaho, is trying to figure out how many salmon a local hatchery should release annually in order to revitalize the fishery. She knows that ifpksalmon spawn in Redfish Lake in a given year, then only 0.2pkfish will return to the lake from the offspring of that run, because of all the dams on the rivers between the sea and the lake. Thus, if she adds the spawn from h fish, from a hatchery, then the number of fish that return from that run k will be pk+1=0.2(pk+h)..

(a) Show that the sustained number of fish returning approaches pโˆž=hโˆ‘k+1โˆž0.2kas kโ†’โˆž.

(b) Evaluate pโˆž.

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

See all solutions

Recommended explanations on Math Textbooks

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