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

Geometric series: For each of the series that follow, find the sum or explain why the series diverges.

k=03-25k

Short Answer

Expert verified

The sum of the series is157.

Step by step solution

01

Step 1. Given Information

The given series isk=03-25k.

02

Step 2. Determine if a geometric series 

  • Find the ratio of the consecutive terms.

3-25k+13-25k=-25k+1-k=-25

  • Since the ratio of the consecutive terms is same, the given series is a geometric series with a common ratio r=-25.
03

Step 3. Determine the convergence 

  • Determine the first term and the common ratio.

c=3-250=3r=-25

  • If r<1, the series converges to c1-r.

c1-r=31--25=31+25=157

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