Finding The Sum of an Infinite Geometric Series

[@TheOrganicChemistryTutor]

Sequences - Free Formula Sheet: bit.ly/4eau2KQ Sequences and Series: www.video-tutor.net/sequences.html

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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]

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[@00_002]

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[@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

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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.

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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.

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

[@surelock3221]

You're baked?

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[@-clipz-]

God bless

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

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

[@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!

[@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.

[@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.

[@r0elcompute]

Looking forward to graduating IT with the help of this guy ,such an inspiration !

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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!!

[@kinslayer3609]

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[@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 .

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

[@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

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

[@God-yd8zh]

Thank you sir for teaching my lesson.

[@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

[@yassine321]

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

[@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.

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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 :(

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Thank you! Very straightforward video.

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akutami sensei makes me learn this lesson

[@JustBaileey]

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

[@leumasgrountiez5647]

This helped me since i got confused at my teachers explanation

[@marielle6673]

This makes so much sense now! Thank you!

[@justgab6851]

can we cancel out mixed numbers?

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

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Best guy ever

[@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

[@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.

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

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The Lord has provided us once again

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your methods are good

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Better than my instructor and sloppy notes, Thanks!

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@@niccoloripamonti6501 Yes I have haha, cheers man!

[@noelamassawe1602]

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

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this video has taught me more in 3 minutes then my entire summer school math lesson

[@spandanshakya8031]

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The gift that keeps on giving

[@robynslater95]

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

[@smio400]

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

[@sumsolution1064]

Speechless sir....

[@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!

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Thank you sooooooooo much ❤

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god bless this man

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Love this guy.

[@angusmothusi]

for one of the problems how do you know the value of e??

[@spicy_tomato641]

Sir I have a question why did you multiply by 2 in 1:40? Edit: Now I know why. Im just gonna leave this comment here to remind people that some people are slower than others and thats okay.

[@aki8683]

Wait what's the reason tho?

[@spicy_tomato641]

@@aki8683 because of the 1/2 the denominator is 2

[@aki8683]

@@spicy_tomato641 Ohh okay thanksss

[@queenosas7774]

​@@spicy_tomato641 does that automatically rule out the denominator??

[@spicy_tomato641]

Lets be realistic here. Its been 3 years. I already forgot. AHAHAHAHAHAHA​@@queenosas7774

[@Radon27]

00:02 Finding the sum of an infinite geometric series using a formula 02:20 Finding the sum of an infinite geometric series using common ratio 04:41 Explaining calculation of the sum of an Infinite Geometric Series 07:04 Finding the sum of an Infinite Geometric Series 09:32 Sum of series with exponential terms 12:17 Finding the first term and common ratio of an infinite geometric series 14:45 Summarizing the method to find the sum of an Infinite Geometric Series 17:23 Determining the sum of the infinite geometric series.

[@milenaa_autic]

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.

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You are a legend

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Your a genius 🤧

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

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

[@alexbutterboy9807]

Why did you multiply by 2 at 1:48

[@ryguy2368]

Absolute legend

[@sukhkaur444]

@ 3:55 (second # problem). 3*3*3 is 27. YOU put 9. Please check for the right ans. Let me know

[@sukhkaur444]

SO the answer should be 27.

[@sukhkaur444]

My bad I see you are multiplying not squaring. OMG sorry

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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 😐

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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.

[@iinnamorasii]

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

[@amnajamal4298]

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

[@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??

[@ziokazuma1811]

Why is it raised to two? In (8)/(1-1/2)

[@johnlecavalier6199]

he just multiplied both sides by two. i though it was raised by two at first as well.

[@elijahcota2408]

Thank you

[@muhammadahmadmuhammadahmad77]

Thanku so much sir

[@iskaiah9239]

Thankyou! Very understandable! 💖

[@adanvivero702]

you are a hero

[@Emily-xs8rj]

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

[@NancySam-vd5xh]

Ur the best!

[@effawannie2149]

thank you!!!

[@nifabcy]

I'm having mental breakdown while watching, why did you multiply it by two😭😭😭 on the first ex.

[@Abby-in6tk]

Hopefully you're doing OK but just in case, I believe he multiplied by 2 to make the 1-1/2 easier to visually work with by making all the numbers whole (i.e 1-1/2 -> 2-1). So instead of having a fraction in the denominator, he has all whole numbers. Technically it was easy to solve without doing so, but I think it looks cleaner that way when explaining

[@victorcastrellon4880]

great video, than you

[@zonborromeo6867]

Please pray for me for my calculus exams tomorrow 😭

[@cesarrivas2295]

How’d you do

[@therohan1957]

Well sir I might just actually pass this test

[@Padmavathyssolution]

Can we say, When the sum is finite, the series is convergent?

[@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

[@DuplicacionesCentroEstudiante]

in the first one, how come the sum is less than the initial value if there is no negative numbers in the series?