This man is a gift to humanity! 😆 I love how he takes time to point things out any sensible person would just accept as given and breeze over. 👍Thank you!
Was feeling anxiety going into this. Im happy to say I understand now. Nothing to be afraid about. You're a wonderful teacher, please keep up the good work!
the best teacher ever. I am learning java from his website and it is great. I watched some of his math videos and he is unbelievably good. Thanks a lot from all my hart.
@@MathAndScience Sir do u realize that how much i have been searching all over the youtube for this topic! You saved ma life sir and I just didnt seem to get this vid and tmrw is my quiz too hopefully goes well👍
This is a wonderful math teacher who can teach math to me easily since he's very experienced Prof! He taught to me more about high math,thank you very much.
In the60s engineering cirrculum the general idea of sequence, series was presented and executed in a matter of seconds and the student, smart or dumb was expected to digest and assume 100% genius of the topics. Unhappily I was the "dumb." Now after watching these presentations by this gentleman, I want my $410/semester tuition back for all the eight courses In the two semesters I attended at U of M. The problem was not me, but the instructors. These people were ineffectual and presumptive. This man on these and many other courses obviously has been gifted my expert knowledge of many subjects, but also quite adept at teaching in a simple clear concise manner. He breaks esoteric subjects down into simple ideas and equations that anyone can understand. Moreover and importantly, he developes the interest in furthering their education. I especially enjoyed his videos on Laplace Transforms and Elementary Differential Equations. It is my wish that he would write a text and name it Higher Mathematics for Scientists and Engineers, a similar title used by Ivan Sokolnoff. The difference between the two texts would be this author's text would be understandable for us dumb engineers.
whenever possible, it's helpful to define infinite series using recursion. you can just solve for its value in most cases: S = 1 + (1/2)S. (1-(1/2))S = 1. (1/2)S = 1. S=2. S= (1/2)^0 + (1/2)^1 + (1/2)^2 + ... + (1/2)^n + (1/2)^(n+1) S. = 1 + 1/2 + 1/4 + 1/8 + ... + 1/(2^n) + (1/2)^(n+1)S. Note that the last term is multiplied times S. It's the tail of S expanded n times. But something AMAZING happens if you are careful. S isn't really the value. If the tail of the recursion goes to zero S = Sum(S,n), when n goes to infinity, because Tail(S,n) goes to zero. S = Sum(S,n) + Tail(S,n). This lets you calculate the closed form formula for n terms! S - Tail(S,n) = Sum(S,n). S - (1/2)^(n+1)S = Sum(S,n). S(1 - (1/2)^(n+1)) = Sum(S,n). 2(1 - (1/2)^(n+1)) = Sum(S,n). 2 - (1/2)^n = Sum(S,n). try it out... adding the first 4 terms 0..3 replacements is... Sum(S,3) = 1/1 + 1/2 + 1/4 +1/8 = 15/8 = 2-(1/2)^3 = 2 - (1/8) = (2*8-1)/8 = 15/8 I honestly have no idea how people figure out most infinite series closed forms without using recursion. Note the sum like 1/2 + 1/4 + 1/8 + ... = 1: S = 1/2 + 1/2 S. 2S = 1 + S. S = 1. S = 1/2 + 1/2 (1/2 + 1/2 S) = 1/2 + 1/4 + 1/8 + ... + 1/(2^n) + 1/(2^(n+1))S. and this to top it off: S = 0.9 + 0.1 S 10 S = 9 + S 9 S = 9 S = 1 S = 1 = 0.9 + 0.1(0.9 + 0.1 S) = 0.9 + 0.09 + 0.01(0.9 + 0.1 S) = 0.9999.... And this works perfectly well for divergent series like "-1 = 1+2+4+8+...", where it is very clear what's going on. S=Sum(S,n) only when Tail(S,n) is zero; S is an important number in calculating the closed form; and is not necessarily the total. It is part of the recursive definition that replaces infinite iteration. -1/12 = S -1 = 12 S 1 = -12 S 1 = (1-13)S 13 S + 1 = S S = 1 + 13 S = 13^0 + 13 S = 13^0 + 13(13^0 + 13 S) = 13^0 + 13^1 + 13^2 + ... + 13^n + 13^(n+1) S subtract the tail, and you have a formula for the first 13 powers. more generally... A = 1 + x A (1-x)A = 1/(1-x) When you differentiate this, you get the famous "-1/12 = 1+2+3+4+..." strange sequence. It is no paradox though because S isn't the value. S-Tail(S,n) is the value, and that goes to infinity as n goes to infinity, and it gives you the n(n+1)/2 formula, in case you didn't know it.
Great lesson👍. Bonus sad lesson included. I should have verified parts two and three being posted before watching this. Now i have to start over somewhere else.
Nice video truly but I have a doubt why should we call it finite series in arithmetic series when we can also add an infinite amount of numbers same as in infinite series?
The sum of the first 5 terms of a G.P is 4 and the sum of the terms from the fourth to the eighth inclusive is 125/16. Find the common ratio and the sixth term.
here use it in a header file in c++ or make a void function in c#, java or whatever int Sum(int iniVal, int count, int step) { int result = 0; for (int n = iniVal; n
It’s not on the site yet. Just released this lesson for free on UA-cam. I’m working on the rest along with worksheets and quizzes to go with these lessons. There are many more forthcoming for members!
@@MathAndScience yes.. i was a member before.. I was too busy with work and cancelled but now I am ready to join again. I was wondering if this was pre-calculus or Algebra.. Thanks for getting back to me.
Einstein's theory of General Relativity when mentioned in polite conversation is talked about as time slows down as you approach the speed of light. WTF
Thank you so much for refreshing my brain. I found you when I'm retired. Do we know-how this knowledge came from? I just start my channel not long ago, please check it out, I'll appreciate it, thanks.
This man is a gift to humanity! 😆 I love how he takes time to point things out any sensible person would just accept as given and breeze over. 👍Thank you!
This man is a gift to humanity! 😆 I love how he takes time to point things out any sensible person would just accept as given and breeze over. 👍Thank you!
![The Arithmetic Series - Part 1 - [14]](http://i.ytimg.com/vi/7Weu-TwS-S0/mqdefault.jpg)
This man is a gift to humanity! 😆 I love how he takes time to point things out any sensible person would just accept as given and breeze over. 👍Thank you!
Was feeling anxiety going into this. Im happy to say I understand now. Nothing to be afraid about. You're a wonderful teacher, please keep up the good work!
the best teacher ever. I am learning java from his website and it is great. I watched some of his math videos and he is unbelievably good. Thanks a lot from all my hart.
Wow, thanks!
@@MathAndScience Sir do u realize that how much i have been searching all over the youtube for this topic! You saved ma life sir and I just didnt seem to get this vid and tmrw is my quiz too hopefully goes well👍
This instructor makes life with maths so easy! I am preparing for my college algebra (clep) and your videos are very very helpful. Thanks Mr Jason
Happy to help!
AMAZING! So glad I found this channel 😀Phenomenal teacher.
Thanks professor.
Your explanation is amazing and shows extraordinary teaching experience
I cannot emphasize enough how amazing was your explanation of the topic ,, Thanks a lot
I wish you keep doing such a great job
This is a wonderful math teacher who can teach math to me easily since he's very experienced Prof!
He taught to me more about high math,thank you very much.
I love you start with the derivations unlike other UA-camrs who go straight to the formula
Perfect explanation thank you. I'm self teaching linear algebra, calculus, and more advanced math - I find your tutorials just gold.
from online school i can’t learn anything your videos are a huge help thank you
In the60s engineering cirrculum the general idea of sequence, series was presented and executed in a matter of seconds and the student, smart or dumb was expected to digest and assume 100% genius of the topics. Unhappily I was the "dumb." Now after watching these presentations by this gentleman, I want my $410/semester tuition back for all the eight courses In the two semesters I attended at U of M. The problem was not me, but the instructors. These people were ineffectual and presumptive. This man on these and many other courses obviously has been gifted my expert knowledge of many subjects, but also quite adept at teaching in a simple clear concise manner. He breaks esoteric subjects down into simple ideas and equations that anyone can understand. Moreover and importantly, he developes the interest in furthering their education. I especially enjoyed his videos on Laplace Transforms and Elementary Differential Equations. It is my wish that he would write a text and name it Higher Mathematics for Scientists and Engineers, a similar title used by Ivan Sokolnoff. The difference between the two texts would be this author's text would be understandable for us dumb engineers.
If only more professors would quit professing and actually teach like this. You are an amazing teacher!
This was awesome! I'm having trouble finding Part 2 to see the other direction of going from series to summation notation?
Thank you sir you have made this topic really simple
Wonderful way to teach here. I loved it. Thanks a lot sir.
I am from Nepal😊😊
hand down the best maths teacher!!!!!
Excellent content you are a very gifted teacher sir!!!
just spent the last 2 hours trying to figure out what you explained in 2 minutes, thank you
Outstanding explanation ❤.
Gosh, I really want him to teach in my school. By the way, I'm from the Philippines. You just increased my passing points, sir. Thank you so much!!
This video has made it clear ❤
Clearly explained Sir.. Thanks for the knowledge you imparted to me..
whenever possible, it's helpful to define infinite series using recursion. you can just solve for its value in most cases:
S = 1 + (1/2)S.
(1-(1/2))S = 1.
(1/2)S = 1.
S=2.
S= (1/2)^0 + (1/2)^1 + (1/2)^2 + ... + (1/2)^n + (1/2)^(n+1) S.
= 1 + 1/2 + 1/4 + 1/8 + ... + 1/(2^n) + (1/2)^(n+1)S.
Note that the last term is multiplied times S. It's the tail of S expanded n times. But something AMAZING happens if you are careful. S isn't really the value. If the tail of the recursion goes to zero S = Sum(S,n), when n goes to infinity, because Tail(S,n) goes to zero.
S = Sum(S,n) + Tail(S,n).
This lets you calculate the closed form formula for n terms!
S - Tail(S,n) = Sum(S,n).
S - (1/2)^(n+1)S = Sum(S,n).
S(1 - (1/2)^(n+1)) = Sum(S,n).
2(1 - (1/2)^(n+1)) = Sum(S,n).
2 - (1/2)^n = Sum(S,n).
try it out...
adding the first 4 terms 0..3 replacements is...
Sum(S,3) = 1/1 + 1/2 + 1/4 +1/8 = 15/8
= 2-(1/2)^3 = 2 - (1/8) = (2*8-1)/8 = 15/8
I honestly have no idea how people figure out most infinite series closed forms without using recursion.
Note the sum like 1/2 + 1/4 + 1/8 + ... = 1:
S = 1/2 + 1/2 S.
2S = 1 + S.
S = 1.
S
= 1/2 + 1/2 (1/2 + 1/2 S)
= 1/2 + 1/4 + 1/8 + ... + 1/(2^n) + 1/(2^(n+1))S.
and this to top it off:
S = 0.9 + 0.1 S
10 S = 9 + S
9 S = 9
S = 1
S = 1
= 0.9 + 0.1(0.9 + 0.1 S)
= 0.9 + 0.09 + 0.01(0.9 + 0.1 S)
= 0.9999....
And this works perfectly well for divergent series like "-1 = 1+2+4+8+...", where it is very clear what's going on. S=Sum(S,n) only when Tail(S,n) is zero; S is an important number in calculating the closed form; and is not necessarily the total. It is part of the recursive definition that replaces infinite iteration.
-1/12 = S
-1 = 12 S
1 = -12 S
1 = (1-13)S
13 S + 1 = S
S = 1 + 13 S
= 13^0 + 13 S
= 13^0 + 13(13^0 + 13 S)
= 13^0 + 13^1 + 13^2 + ... + 13^n + 13^(n+1) S
subtract the tail, and you have a formula for the first 13 powers.
more generally...
A = 1 + x A
(1-x)A = 1/(1-x)
When you differentiate this, you get the famous "-1/12 = 1+2+3+4+..." strange sequence. It is no paradox though because S isn't the value. S-Tail(S,n) is the value, and that goes to infinity as n goes to infinity, and it gives you the n(n+1)/2 formula, in case you didn't know it.
how can someone be this talented at teaching
Thank you for making maths 😊 easy for me
9:11
In order for you to get to 1 you have to get to 1/2 before that 1/4 before that 1/8 etc
Therefore ......
sum of (1/2+1/4+1/8...)=1
The Best Teacher!
You made it so easy to understand! Thanks a lot!
You're welcome!
This lesson was super helpful.Thank you. 😃
It would be great if you had links or names of the previous lessons you mentioned!
YOU ARE THE BEST!!!!!!!!!!
Thank you so much...i have exam this Monday and our teacher told us nothing about sigma, but this though me everything
I so love your videos!!! THANK YOU!!!
So clear Sir, thank you
Great lesson👍. Bonus sad lesson included. I should have verified parts two and three being posted before watching this. Now i have to start over somewhere else.
I couldn't find the video where you show how to calculate the series. Will you upload it in the future?
welcome back wonderful lesson
Great work sir
Nice video truly but I have a doubt why should we call it finite series in arithmetic series when we can also add an infinite amount of numbers same as in infinite series?
You are the best of the best !!
The sum of the first 5 terms of a G.P is 4 and the sum of the terms from the fourth to the eighth inclusive is 125/16. Find the common ratio and the sixth term.
He is my hero 🎉
To be honest superb lecture 💯
Thank you sooo much
Sir i do not understand the should be the base of a number is that right ?
This man should be getting my tuition fee
Easily Solved. explained in detail. i liked your channel. thank you and congrats
I #BrainBlitzAudios appreciate explanation. 😊😊😊😊💜💙💜💙💜💙💜
What if the expression's has negative and positive, example like 1-2+3-4+5
here use it in a header file in c++ or make a void function in c#, java or whatever
int Sum(int iniVal, int count, int step)
{
int result = 0;
for (int n = iniVal; n
Where can I find part 2 of this video?
Please explain fractional binomial
I've always wondered what those sigmas were all about. Now I finally know.
Really great, thank you
What you noticed finally
So impressive 🤞
11:08
im really waiting for part 2 ... pls do part 2 pls
I couldn't find the next video. Can someone help?
9:11 listen to ted ed (zenos paradox) then keep on watching.
Accuracy is important than perfection. Eventhough we are perfect in many aspects,we are not quite sure of its accuracy.
thank you!
he needs more attention tbh
What category is this under on your site. I looked for it but couldn't find it..
It’s not on the site yet. Just released this lesson for free on UA-cam. I’m working on the rest along with worksheets and quizzes to go with these lessons. There are many more forthcoming for members!
@@MathAndScience yes.. i was a member before.. I was too busy with work and cancelled but now I am ready to join again. I was wondering if this was pre-calculus or Algebra.. Thanks for getting back to me.
Love you
Thanku very much!
Is the increment for k always 1?
Ok, I was with you until you got to 28:41…. How does 2 to the 3rd power give you 8 and etc? I got lost there.
Yes
where can i find the next part?
The Pest teacher 🧑🏫
Where is part 2?
Einstein's theory of General Relativity when mentioned in polite conversation is talked about as time slows down as you approach the speed of light. WTF
Actually what you refer to is called “special relativity”. General relativity is the theory of gravity. Time flows different in a gravitational field!
Wer is part 3..?
25:41
part two
Thank you so much for refreshing my brain. I found you when I'm retired. Do we know-how this knowledge came from? I just start my channel not long ago, please check it out, I'll appreciate it, thanks.
I swear I thought this was professor selvig from thor
What the sigma
Ofogog
Sir update the app in android plsss
well explained!🤍 how i wish ive known this earlier.
This man is a gift to humanity! 😆 I love how he takes time to point things out any sensible person would just accept as given and breeze over. 👍Thank you!
Where is the part 2
16:24
This man is a gift to humanity! 😆 I love how he takes time to point things out any sensible person would just accept as given and breeze over. 👍Thank you!
Where is part 2?