Finding The Sum of an Infinite Geometric Series

This calculus video tutorial explains how to find the sum of an infinite geometric series by identifying the first term and the common ratio. The examples and practice problems are presented using sigma notation or summation notation.
Access Full-Length Premium Videos: / mathsciencetutor
_______________________________________________________________________________________________
Algebra For Beginners: • Algebra For Beginners ...
Algebra 1 Review Study Guide: • Algebra 1 Review Study...
Algebra Final Exam Review: • Algebra Final Exam Review
Pre-Calculus Final Exam Review: • Precalculus Final Exam...
________________________________________________________________________________________________
How To Evaluate Algebraic Expressions: • How To Evaluate Algebr...
Fractions - Basic Introduction: • Fractions Basic Introd...
How To Solve Linear Equations: • How To Solve Linear Eq...
Linear Equations - Test Review: • Linear Equations - Alg...
How To Factor Trinomials: • Factoring Trinomials T...
Systems of Linear Equations - 2 Variables: • Solving Systems of Equ...
Quadratic Equations - Test Review: • Quadratic Equations Mu...
Multiplying Rational Expressions: • Multiplying Rational E...
Graphing Rational Functions: • Graphing Rational Func...
Radical Expressions - Test Review: • Simplifying Radical Ex...
Logarithms Practice Problems: • Logarithms - Practice ...
Functions and Graphs - Practice Problems: • Functions and Graphs |...
How To Graph Equations in Algebra: • How To Graph Equations...
Functions - Test Review: • Functions
________________________________________________________________________________________________
Conic Sections - Basic Introduction: • Conic Sections - Basic...
Finding The Radius and Center of a Circle: • How To Find The Center...
Writing Equations and Graphing Circles: • Graphing Circles and W...
Writing Equations of Ellipses: • Writing Equations of E...
Circumference of an Ellipse: • Circumference of an El...
Area of an Ellipse: • Area of an Ellipse
Eccentricity of an Ellipse: • Eccentricity of an Ell...
Hyperbolas - Conic Sections: • Hyperbolas - Conic Sec...
Parabolas - Focus and Directrix: • Finding The Focus and ...
How To Find The Vertex of a Parabola: • How To Find The Vertex...
Conic Sections Quiz: • Conic Sections Quiz - ...
________________________________________________________________________________________________
Arithmetic Sequences: • Arithmetic Sequences a...
Geometric Sequences: • Geometric Series and G...
The Fibonacci Sequence: • Mathematics - Fibonacc...
Arithmetic, Geometric, & Harmonic Mean: • Arithmetic Mean, Geome...
Probability - Basic Intro: • Introduction to Probab...
Intro to Statistics: • Introduction to Statis...
_______________________________________________________________________________________________
GPA Calculator: • How To Calculate Your ...
Student Loans: • How To Calculate Your ...
Save Money In College: • How To Save Money and ...
SAT Test Prep: • Evaluating Functions a...
ACT Test Prep: • ACT Math Test Prep

[@TheOrganicChemistryTutor]

Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Arithmetic Sequences: kzbin.info/www/bejne/o6moenmFbduLgbs Geometric Sequences: kzbin.info/www/bejne/sHuoiJavqKaWapY

[@-clipz-]

God bless

[@ytman-lq2mj]

n

[@killallpikles3243]

seriously i just come to this guy for everything i’m learning

[@zeyad7947]

i swear to God thats the same with me, even for physics and chemistry.... and especially math now, cuz these online lectures really be crappy as hell so at one point i just ditched the lectures and started watching this guy's videos instead, and i ended up with an A+ in Calc 1. this dude's great!

[@thepeeps191]

Ikr

[@frijolex2509]

Same. This is my go to for anything science/math related.

[@reignhard4696]

Same. My math grade went up from C to B because of these videos, and I was procrastinating! Imagine if I didn’t procrastinate, I’d probably have an A. These vids are great

[@jabcuber3182]

Same here, best math teacher ever.

[@00_002]

I'm an engineering student and this guy has officially carried me through my first year.

[@dazllc]

you guys take this at university? im in 11th grade lmao

[@00_002]

@@dazllc Most uni's re-teach to make sure students are on the same level. I wish I didnt have to fork out 500CAD to learn this stuff xD. You're lucky

[@ezramantini8078]

@@00_002 I’m in my final highschool year. This guy is gold

[@mwu365]

@@dazllc you're gonna do it again

[@shoumodeepmukherjee8736]

@@dazllc same bruh

[@rexr3306]

I literally saw your first example and explanation and understood it right away while my trash math teacher spent 3 days in class trying it explain this and no one understood I saw your video and got it literally within the first 2 minutes. Why cant teachers teach in effective ways that are easy instead of the crappy traditional methods. Thank You!

[@mullins69]

15:39 how did he get e value

[@daUrbanCyclist]

@@mullins69 Thats the universal value of *e* .Like pi has the value 3.1415 , e has the value 2.718

[@Vin_03]

Atleast your teacher described it but in my case only homework.

[@1S0J1]

same bruv.

[@goodolnonamee]

I know right, my dumbass teacher made it a million times more complicated than it had to be

[@puppies3742]

2 minutes in and you've taught me more than my calc prof and the textbook. I've read this chapter like 5 times and could not understand it. Thank you.

[@chrispinchileshe8557]

You can't go wrong with this lecture. My request is to see your face sir. Because of you I'm a fully baked mathematician.

[@adityabhardwaj3495]

for real! I always watch his videos after my school and tuitions just to properly grasp the topic

[@surelock3221]

You're baked?

[@KJ-rc6qs]

Omfg you're baked?

[@dulxbe4883]

@@surelock3221 i am

[@-clipz-]

God bless

[@silasj3412]

How did people understand this before Mar 28, 2018

[@adityabhardwaj3495]

I wonder

[@surelock3221]

My grade 11 teacher did a pretty good job teaching this unit actually

[@adityabhardwaj3495]

@@surelock3221 bro, they taught you this topic in the 11th grade? here we just learn continuity in the 11th grade.

[@surelock3221]

@@adityabhardwaj3495 It might have been grade 12, I just realized I can't remember exactly who my teachers were for those classes, or if it was the same person for both

[@kirinvey2649]

@@adityabhardwaj3495 bruh Im learning this for my 9th-grade pre calc final rn smh.

[@sofia9189]

I watched 2 minutes of this video and IMMEDIATELY understood something I've been trying to get for 2 weeks! Thank you so much!!!!

[@andreferreira2693]

I would never graduate if it wasn't OCT's help! This man is single handed forming the future of the world! Thank you Sir!

[@kinslayer3609]

Sir u help me in my need! God bless you!

[@peydee_364]

you're the only reason why I even have a chance at passing my calc 2 midterm tomorrow

[@Aj_chan0130]

bro same i have a test tomorrow this guy is fr the goat. Thanks Teach

[@Benedict_Miriti]

Thank you so much.After watching the lecture video on finding the sum of infinite geometric series, i have been able to complete my assignment.You surely cannot go wrong with this lecturer.

[@Flower-cu5li]

Thank you! Very straightforward video.

[@yassine321]

Thanks a lot i really appreciate those lectures and also the lectures of thermodynamics

[@patrickmayer9218]

1. In the a/(1-r) formula, a is just a sub 1. 2. The abs(r) < 1 is just a check to see if you can use the a/(1-r) formula.

[@monishjain1113]

A whole day of not understanding my Calculus professor and textbook, and this video taught me all of it within 15 mins! Many thanks!

[@ComputerCurry]

This doesn't look as difficult as I previously thought. Thanks!

[@konabos747]

Thank you for helping so many college students throughout the years. I am so grateful for this channel's existence and I owe my college degree to you.

[@carolyndokes5350]

I'm a high school math teacher, and this guy is ' my go to'. Thank you

[@juulia287]

dude is literally my life saver. I have a math final on Tuesday on this lesson, this will rly help me

[@Rawya-te4fs]

I want to express my sincere gratitude for your exceptional videos on organic chemistry. I struggled with mathematics, but thanks to your expert guidance, I was able to achieve an A in both Calculus 1 and Calculus 2. Your teaching has made a significant difference in my academic performance. Thank you for being the best! If you need any further adjustments, feel free to let me know!

[@DaiMoscv]

14:36 there is easier way, if SUM(n=m) then (ar^m)/1-r. So in our case our m = 1, a = 5, r = 8/25. If you follow the equation you'll get same answer as in the video 40/17 .

[@arnoldtaiwo5604]

u need a noble price for this u are like a life saver and also a hero

[@God-yd8zh]

Thank you sir for teaching my lesson.

[@bepositive3514]

Thank you very much for this great video🤩

[@vampsog7605]

Thank you sir, you are a life saver.

[@jossadesamito9552]

THANK YOU SO MUCH! ❤️

[@RRatedT]

Thank you so much, I finally understand what I'm suppose to do.

[@hopeschroder8122]

thank you very much ,this helped out a lot

[@eliseerickson5994]

I looked at my calc notes today for a test and nothing made sense after a month. I don't ever remember my teacher explaining it like this but I finally understand something!!

[@marielle6673]

This makes so much sense now! Thank you!

[@justgab6851]

can we cancel out mixed numbers?

[@noelamassawe1602]

Your content are amaizing

[@ricric4722]

I don't think you'll ever be able to comprehend just how many lives you're constantly positively impacting

[@xeli3046]

To all further maths students: do you know the feeling when you've already studied a subject like this and then forgetting what you've learned years after the years??? Yeah, that's how I feel rn :(

[@justsam0511]

But it's like riding a bike. We can get back on easier second time.

[@drumman22]

@@justsam0511 maybe not quite like a bike but it's definitely easier to pick back up the next time around

[@77R_]

@@justsam0511 Except the bike breaks apart if you switch a sign accidentally.

[@_Cfocus]

nope just nope its suffering and suffering only@@justsam0511

[@tonyha8888]

We also have the same question. and if you factorised the numerator on the last question into 2^n(2^2+1)/5^n this simplified to 5(2/5)^n and we obtained a different answer which was 10/3

[@VILOHIT]

your methods are good

[@damsellette]

akutami sensei makes me learn this lesson

[@nelsonphiri7914]

This guy is the best.

[@AnanomousRex]

your a legend bro, love you very much

[@AlexRose-qd3or]

Thank you so much for all of the math tutorials you've made, they've helped so much. Do you think you can make your voice a little bit louder though? It gets hard to hear your explanations any time there's even a little bit of background noise.

[@eric3996]

Thank you!

[@user-cd5fp9zi6t]

i am first year civil E student and this guy really make me HAPPY love you big man

[@mahidertihtina4852]

Love this guy.

[@sumsolution1064]

Speechless sir....

[@masonwong895]

This is a really good video!!!!!!!!!!!!!!!!

[@aymanhijjawi9869]

I watched this and now I'm a mathematician by genetics !

[@A_B_1917]

Pro tip about the (2^3n)*(5^1-2n). When you get to the point where there is sigma of "5*(8/25)^n" you actually CAN use formulas. You can tranform it into "5*(8/25)*(8/25)^(n-1)", so that it fits formula with sigma starting from 1.

[@sandilemposula3538]

How do you do that, please send me via e-mail.My e-mail is [e-mail] m writing this Monday.

[@Notthisagain28]

This will NOT give you the same answer which is 40/17. This instead gives you 200/17. WRONG ANSWER

[@SuperG3FR]

Best guy ever

[@mochii1908]

i always go to this guy whenever there's a lesson I can't understand from my teacher..

[@leumasgrountiez5647]

This helped me since i got confused at my teachers explanation

[@anipurasu]

Thank you sooooooooo much ❤

[@nishadr.7637]

I understood everything in the first 3 minutes, this is a very helpful video

[@JustBaileey]

Exactly what I was looking for. I can make the assumption that if r>1 the series must be diverging.

[@elijahcota2408]

Thank you

[@spandanshakya8031]

love you mate

[@aashsyed1277]

3 m subscribers!!!!! I'm excited!!!

[@carsonbarnes1834]

god bless this man

[@muhammadahmadmuhammadahmad77]

Thanku so much sir

[@geektoys370]

You are a legend

[@AlbertoRivas13]

thanks bro

[@phelhadsu4080]

your students must be so lucky to have you

[@user-cd8su1oe9m]

May God bless you i have no word for you

[@effawannie2149]

thank you!!!

[@-avalon-9440]

This guy is way more useful then my teacher

[@victorcastrellon4880]

great video, than you

[@niccoloripamonti6501]

my worst fear is that one day I will have to learn something that you havent covered on the channel :(

[@issachernandez1828]

Better than my instructor and sloppy notes, Thanks!

[@ryguy2368]

Absolute legend

[@noelamassawe1602]

Please can you do a video About expansion of e^x To find sum of geometric series using e^x

[@iskaiah9239]

Thankyou! Very understandable! 💖

[@Kasfas]

I’ve been trying to get this for days now and only now understood it. I’m going to keep this one stored away for future reference.

[@malxruxes6704]

The gift that keeps on giving

[@jimdolloso2331]

Your a genius 🤧

[@sunduspp7123]

sir your lectures are awesome but can you make it a bit louder [it is less audible]

[@amnajamal4298]

Can you please explain how you come to the exponential number at the end?

[@yixuhoon6125]

Hey can you make a playlist on linear algebra.. Space and base staff

[@NancySam-vd5xh]

Ur the best!

[@skilledkitty3623]

Thank you 🙏🏻

[@user-ii2mm9zm7d]

so in the first example why did you multiply both 8 and 1-1/2 by 2

[@queenosas7774]

Thank you so much but d part not yet clear for me is when we multiple both side with the denominator does that automatically rule out the denominator itself??

[@robynslater95]

I like these series because you can see what it will converge to if it does

[@jeloespiritu8084]

how did you get the 2?

[@milenamijuskovic2340]

You are literally saving me, but can you please please do one where r is bigger than one? For example idk how to solve; sigma( 1 to infiity) of 1^n/(n^6) -_-' :(

[@WittyComm3nter]

I know you're progabaly not concerned with this answer anymore. But that's a p series not a geometric series. the P value (which is 6) is > 1 so it converges by p series test. According to the online calculator wolfram alpha it converges to 1.0173..... wolfram alpha used comparison test.

[@fitnessabdul6811]

@@WittyComm3nter Ok.

[@user-sr1pp7sv9q]

You might’ve just saved me from failing my exam tomorrow. Fingers crossed.

[@chad4751]

nice.

[@Emily-xs8rj]

In the first example, why do you square the 8/(1-1/2)?

[@dejabu24]

question : how do you know that the series has the same patter all the way to infinity by only testing a couple of those numbers Im referring to r , thanks you for sharing

[@alexbutterboy9807]

Why did you multiply by 2 at 1:48

[@adanvivero702]

you are a hero

[@abdomuse9953]

what do you do when n>1?

[@giftykusi513]

How do you find the sum to infinity when the common ratio is greater than 1?

[@ItsMeLucke_Studio]

What if a1 would be a fraction along with r being a fraction? How would that work?

[@hluke7793]

I need your help with this problem : The second term of a sequence is 17 and the sum of the first six terms is 147 : Determine the first three terms and the nth term. .. Please help me. ...if you have a video referring to this problem may you please give me the link.

[@arvindkannan867]

thank you so much. I do have a doubt though. in the last problem, why did you split the fraction as 4/5 + 2/5?? why couldn't we solve without splitting the fraction? like then , first term would then be 6/5 and common ratio would be 2/3 and the total sum then would be 18/5. can you please clarify?

[@tonyha8888]

We also have the same question. and if you factorised the numerator on the last question into 2^n(2^2+1)/5^n this simplified to 5(2/5)^n and we obtained a different answer which was 10/3

[@jimhalpert9803]

I tried without splitting and it wasn't forming a geometric series as the r differed in value when I tried a2/a1 and a3/a2

[@morganblarue]

@@jimhalpert9803 YES. This was my question. Thank you, Jim, for explaining!

[@ignasxv]

good

[@panagiota4298]

Can someone help? I'm trying to solve this: Σ=n/(3^n) from 1 to infinity and the common ratio isn't the same when i try to validate it

[@ST-od1br]

Btw KZbin keep adding adds telling students that they can get better education by leaving KZbin education channels that can destroy your work .. just saying 😐

[@kameronbriggs235]

Yeah but anyone who follows these, knows they are great. I got like almost 170 videos of his down, and im going to finish this entire calculus playlist of 226. People are here for a reason.

[@mouaad2322]

What if there is a minus sign in front of r?

[@scottsvedin7065]

Why did he multiply he two?

[@georgesadler7830]

Professor Organic Chemistry Tutor, thank you for explaining The Sum of an Infinite Geometric Series in Calculus Two. Geometric Series are very important in Advanced Mathematics/Engineering. Geometric Series is also used in Signal and Systems Theory and Digital Signal Processing. This is an error free video/lecture on KZbin TV with the Organic Chemistry Tutor.