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

Find a series k=1akwith all non - zero terms that converges to 1 ,

Short Answer

Expert verified

Series converges to 1 .

Step by step solution

01

Step 1. Given information 

We have been given a seriesk=1akand to find out the convergence of series .

02

Step 2. Checking whether the series is convergent .

Consider the series k=1ak

The objective is to find the geometric series k=1akwith all non zero terms

Consider the series k=1ak=k=112k

The series is a geometric series with geometric ratio 12which is less than 1.

The series with geometric ratio less than 1 is convergent in nature .

Therefore ,k=1ak=k=112kis convergent .

03

Step 3. Value of convergence 

The series converges k=1ak=k=112kto

role="math" localid="1649674645349" S=12112=1212

=1

Hence the series converges to1

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