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

In Exercises 29–34 use the ratio test to analyze whether the given series converges or diverges. If the ratio test is inconclusive, use a different test to analyze the series.

k=15kk5.

Short Answer

Expert verified

The series diverges.

Step by step solution

01

Step 1. Given information.

The given series isk=15kk5.

02

Step 2. Ratio test.

According to the given series,

ak+1ak=5k+1(k+1)55k(k)5=(k)55k+1(k+1)55k=5(k)5(k+1)5

03

Step 3. Conclusion.

On taking limits,

limkak+1ak=limk5(k)5(k+1)5=5limk(k)5(k+1)5=5limk(k)5(k)51+1k5=5×1=5Since,L>1,

Therefore, the series diverges.

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