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

Prove the root test. You may model your proof on the proof of the ratio test

Short Answer

Expert verified

g

Step by step solution

01

Step 1.

gggggggg

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

An Improper Integral and Infinite Series: Sketch the function f(x)=1xfor x โ‰ฅ 1 together with the graph of the terms of the series โˆ‘k=1โˆž1k.Argue that for every term Snof the sequence of partial sums for this series,Sn>โˆซ1n+11xdx. What does this result tell you about the convergence of the series?

Determine whether the series โˆ‘k=0โˆž2k+25k-1converges or diverges. Give the sum of the convergent series.

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

0.199999...

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

3.454545...

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