Finding The Sum of an Infinite Geometric Series
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- Опубликовано: 9 сен 2024
- 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.
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you guys take this at university? im in 11th grade lmao
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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!
15:39 how did he get e value
@@mullins69 Thats the universal value of *e* .Like pi has the value 3.1415 , e has the value 2.718
Atleast your teacher described it but in my case only homework.
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How did people understand this before Mar 28, 2018
I wonder
My grade 11 teacher did a pretty good job teaching this unit actually
@@surelock3221 bro, they taught you this topic in the 11th grade? here we just learn continuity in the 11th grade.
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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.
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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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.
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If you need any further adjustments, feel free to let me know!
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.
How do you do that, please send me via e-mail.My e-mail is smposula300@gmail.com.Please m writing this Monday.
This will NOT give you the same answer which is 40/17. This instead gives you 200/17. WRONG ANSWER
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Thank you! Very straightforward video.
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
Why did you multiply by 2 at 1:48
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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) -_-' :(
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.
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I understood everything in the first 3 minutes, this is a very helpful video
Exactly what I was looking for. I can make the assumption that if r>1 the series must be diverging.
Please can you do a video
About expansion of e^x
To find sum of geometric series using e^x
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I like these series because you can see what it will converge to if it does
This makes so much sense now! Thank you!
can we cancel out mixed numbers?
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 RUclips TV with the Organic Chemistry Tutor.
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.
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?
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
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
@@jimhalpert9803 YES. This was my question. Thank you, Jim, for explaining!
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so in the first example why did you multiply both 8 and 1-1/2 by 2
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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??
Can you please explain how you come to the exponential number at the end?
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In the first example, why do you square the 8/(1-1/2)?
Absolute legend
What if a1 would be a fraction along with r being a fraction? How would that work?
Thank you
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Thanks, but I can't find what to do in the case that a = n.
The gift that keeps on giving
in the first one, how come the sum is less than the initial value if there is no negative numbers in the series?
Thank you!
how did you get the 2?
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
great video, than you
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.
Wait what's the reason tho?
@@aki8683
because of the 1/2 the denominator is 2
@@spicy_tomato641 Ohh okay thanksss
@@spicy_tomato641 does that automatically rule out the denominator??
Lets be realistic here. Its been 3 years. I already forgot. AHAHAHAHAHAHA@@queenosas7774
Why did he multiply he two?
Your a genius 🤧
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.
please someone suggest me a good video or channel from where I can cover the topic of complex analysis and problems related to curves, lines etc....
Can we say, When the sum is finite, the series is convergent?
15:30 - Didn't you say earlier in this video that the summand's power should be (n-1) if n starts from 1, and should be n if n starts from 0? Why the power = n here while n starts from 1? That is, the a₀ term is missing.
thanks bro