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

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.

k=11k2

Short Answer

Expert verified

The divergence test failed as limk1k2=0.

Step by step solution

01

Step 1. Given information.

Consider the given series,

k=11k2

02

Step 2. Analyze the series.

The divergence test states that if the sequence akdoes not converge to zero, then the series akk=1diverges.

The value of the sequence ak=1k2is given below,

limkak=limk1k2=0

Thus, the divergence test failed aslimk1k2=0.

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

Study anywhere. Anytime. Across all devices.

Sign-up for free