Sum of Infinite Geometric Series

We discuss how to find the sum of an infininte geometric series that converges in this free math video tutorial by Mario's Math Tutoring. We also discuss when the series diverges and the sum cannot be found. We also look at some example problems.
0:30 Formula for the Sum of an Infinite Geometric Series
0:44 Restrictions for being able to find the Infinite Sum
1:00 Difference between Convergent and Divergent Series
1:29 Example 1 Finding the Sum of a Convergent Geometric Series
2:28 Example 2 How to calculate the Ratio of a Geometric Series and calculate the Sum.
Related Videos:
Sum of a Finite Geometric Series
• Sum of a Geometric Series
Sum of an Arithmetic Series
• Sum of an Arithmetic S...
Looking to raise your math score on the ACT and new SAT?
Check out my Huge ACT Math Video Course and my Huge SAT Math Video Course for sale at
mariosmathtutor...
For online 1-to-1 tutoring or more information about me see my website at:
www.mariosmatht...
* Organized List of My Video Lessons to Help You Raise Your Scores & Pass Your Class. Videos Arranged by Math Subject as well as by Chapter/Topic. (Bookmark the Link Below)
www.mariosmatht...

[@MariosMathTutoring]

If you want a good review of sequences and series(arithmetic and geometric) see my review video on the topic here: kzbin.info/www/bejne/ipubanl3YsljnJo

[@FuzzzyJunior]

Learning online has been a struggle and this video was extremely clear and concise. Thank you so much for helping me!

[@MariosMathTutoring]

You’re welcome! Glad my video helped you!

[@tirzahbruski5871]

I am a teacher, teaching from home. Thank you for producing a video that will help my students understand the sums of infinite geometric series.

[@MariosMathTutoring]

You’re welcome Tirzah! Glad to hear my videos are helping your students!

[@anonymoususer5393]

Thanks, my doubt got cleared within 2 minutes. Amazing.

[@stellarbadger2571]

Just saved me from depression and hours of work😂😂thank youuuu 🙏🏻

[@Prince-jf1nb]

Thanks for teaching

[@Beamthegamer]

Good work sir. Thanks to you I understand. Awesome teacher!

[@MariosMathTutoring]

Glad you like my teaching style and that my videos are helping you!

[@Beamthegamer]

@@MariosMathTutoring :)

[@preethigunarathne3122]

i so agree! #Mr. Mario

[@roneljamesroxas1191]

I want to know how to get common ratio if the given is the sum to infinity and the first term. Can you please tell me

[@jadzakaria7381]

Ronel 1810 bro plug in the numbers and just arrange it to equal r then your good

[@rosette_renah]

This is really good,,thanks

[@narinderkumar4708]

Way of finding 'r' is 👌👌👌 Thank you sir

[@MariosMathTutoring]

You’re welcome Nikhil! Glad my video helped you!

[@kima840]

Thank god for u my teachers on the other hand

[@MariosMathTutoring]

Glad my video helped you Kim!

[@florakettle]

THANK YOU SIR!!!!! YOU MADE MY LIFE EASIER

[@MariosMathTutoring]

Awesome Quelaire! Glad my video helped you!

[@mogli3leo]

You, Sir, are a genius!

[@MariosMathTutoring]

I’m glad my videos are helping you Leo!

[@AbhishekMishra-ci6xe]

Love from India to you.....

[@MariosMathTutoring]

Glad you like my videos Abhishek!

[@a.sathyajothi2580]

Thank you sir.

[@bongo_baller8948]

What if the ratio of the sequence is multiplying by 2 For example: 10,20,40,80 How would you find the infinite sum of it?

[@MariosMathTutoring]

This video I did here will explain your question: Sum of Infinite Geometric Series kzbin.info/www/bejne/m4O1m3d5fdF3rck

[@bongo_baller8948]

Would the answer be no solution? Because one of the questions on my homework was 10,20,40,80, and r=2. It was greater than the -1

[@alemendoza2969]

In the first example you did, did you jist ignored the 1-? Because it was 1-(1/2) but you just multiplied it by 2.. Ignoring the one? Im confused. :(

[@bethanyturner2766]

Ale Mendoza since the denominator is a subtraction, you have to solve the bottom of the fraction first. If it helps, imagine a pair of parentheses around the denominator and solve like you would using BIDMAS or BODMAS. The answer in the parentheses would equal 1/2, so then he divides by 1/2, which is equal to multiplying by 2, to get 200. I hope that helps 😊

[@harry-fl6tf]

nice and short lecture, you saved my ass Professor

[@jenvyclairereplente3825]

What if the ratio of the sequence is more than 1?

[@rosette_renah]

Exactly?Please sir answer this

[@tungsten_disulphide]

Just simply turn the "1-r" at the denominator into "r-1"

[@elrishjohnrull3545]

Gegegegegge thanks

[@shankaraiahkothuri4896]

tq sir

[@MariosMathTutoring]

You’re welcome Shankaraiah!

[@isaacsiame345]

IS 2/3 divergent

[@MariosMathTutoring]

If the ratio is 2/3 then it is convergent.

[@isaacsiame345]

@@MariosMathTutoring Alright thanks

[@k3ns3s53]

How did you get 200?

[@MariosMathTutoring]

When you divide 100 by 1/2 you get 200. When you divide by a fraction it is like multiplying by the reciprocal...hope that helps!

[@k3ns3s53]

@@MariosMathTutoring I didn't get that in my last try Thank you very much

[@MariosMathTutoring]

You’re welcome!

[@kashyapvishnudas1466]

Can u prove it