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

Determine whether the series 803-203+53-512+converges or diverges. Give the sum of the convergent series.

Short Answer

Expert verified

The series 803-203+53-512+converges to643.

Step by step solution

01

Step 1. Given information.

Given a series 803-203+53-512+.

02

Step 2. Find if the series converges or not.

The standard form of a geometric series is k=0crk.

The geometric series converges if and only ifr<1.

In the series 803-203+53-512+it can be seen that c=803.

Every term after that is -14times the previous term.

It follows that r=-14.

Since r=-14, the series803-203+53-512+converges.

03

Step 3. Find the value to which the series converges.

If the geometric series k=0crkconverges, it converges to c1-r.

So, the series localid="1648982757515" 803-203+53-512+converges to localid="1648982761274" 8031--14, that is 643.

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