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.

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}.

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.

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

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99. Greetings....
Check out these credit cards today.
My name is Robert Williams from California. A successful business owner and father. I got one of these already programmed Credit cards that allows me withdraw a maximum of $5,000 daily for 30 days. I am so happy about these cards because I received mine last week and have already used it to get$20,000. Mr frank Richard   of [email protected] is giving out these cards to support people in any kind of financial problem. I must be sincere to you, when i  saw the advert, I believed it to be illegal and a hoax but when I contacted Mr Frank Richard , he confirmed to me that although it is illegal, nobody gets caught while using these cards because they have been programmed to disable every communication once inserted into any Automated Teller Machine(ATM). If interested contact him as soon as possible Email:[email protected]

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115. I am Leah Hart I live in Ohio USA I’m 32 Years old, am so happy I got my blank ATM card from united hacking company  blank ATM card that can withdraw $5,500 daily. I got it from him last week and now I have withdrawn about$15,000 for free. The blank ATM withdraws money from any ATM machines and there is no name on it because it is blank just your PIN will be on it, it is not traceable and now I have money for business, shopping and enough money for me and my family to live on.I am really glad and happy i met united hacking company  because I met Five persons before him and they could not help me. But am happy now united hacking company  sent the card through DHL and I got it in two days. Get your own card from him right now, he is giving it out for small fee to help people even if it is illegal but it helps a lot and no one ever gets caught or traced. I’m happy and grateful to the united hacking company   because he changed my story all of a sudden. The card works in all countries that is the good news contact. email address: [email protected] or whatsApp:  +44 7466 770724

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