Monday, May 13, 2019

Advanced Math Solutions - Series Convergence Calculator, Geometric Series

Series are an important part of Calculus. In this next series of blog posts, I will be discussing infinite series and how to determine if they converge or diverge.

For a refresher:

A series is the sum of a list of terms that are generated with a pattern. A series is denoted with a summation symbol. An infinite series is a series that has an infinite number of terms being added together.

Here is an example of an infinite series:


With infinite series, it can be hard to determine if the series converges or diverges. Luckily, there are convergence tests to help us determine this!

In this blog post, I will go over the convergence test for geometric series, a type of infinite series.

A geometric series is a series that has a constant ratio between successive terms. A visualization of this will help you better understand.

Here’s a geometric series:


In this series, each following term is the product of the prior term and ⅓.

We can rewrite this geometric series using the summation notation.


In order to determine if a geometric series diverges or converges, you’ll need to follow and remember the following test/rule:

If the series is of the form ,

if |r|<1, then the geometric series converges to
if |r|≥1, then the geometric series diverges

Let’s see some examples to better understand.

First example (click here):


1. Reference the geometric series convergence test
         

2. Determine the value of r


3. Determine if the series converges or diverges

                                               The geometric series converges to \frac{5}{4}.

Next example (click here):


1. Reference the geometric series convergence test


2. Determine the value of r


3. Determine if the series converges or diverges

                                                       The geometric series diverges.

Last example (click here):


1. Reference the geometric series convergence test


2. Determine the value of r


3. Determine if the series converges or diverges

                                               The geometric series converges to 6.

As you can see, it is not too difficult to determine if a geometric series converges or not. After doing some practice problems, you’ll get the hang of it very quickly. For more help or practice on geometric series, check out Symbolab’s Practice. Next blog post, I’ll go over the convergence test for p-series.

Until next time,

Leah

3 comments:

  1. The article you have shared here very awesome. I really like and appreciated your work bouncing balls , red ball

    ReplyDelete
  2. Math and English are very predictable and regular in their usage, and the one underlying thing that you require to understand to survive in any profession is how to attack difficulties in an orderly manner to arrive at predictable solutions. If there were any additional subjects that teachers could use to teach you how to.Write My Essay - MakeMyEssay The universal value of math, whether you use it directly or not,

    ReplyDelete
  3. Are you looking for affordable but quality assignment help, before booking your order read this uk essays review.
    Of late it has been seen that students are wondering “is edubirdie legit?”
    Now, does that make Grademiners legit site to work with? Certainly not! What students mostly look for in such cases is security. This certainly Grademiners Review makes a fake site to work with.
    All the scholastic requirements of the higher educational institutions in mind when composing the assignment from scratch. As per the Myassignmenthelp Review posted by students, MyAssignmenthelp.com legit website for expert assistance with assignments.

    ReplyDelete