+Finni M. It's a for loot except you cannot control by what increment the loop's index increases by, it's always 1. However, if you don't use the index in the looped part, but a multiple of it, the porblem can easily be solved, like I did in a random pi calculation formula from pi = 3 + 4/(2*3*4) - 4/(4*5*6) + 4/(6*7*8) - 4/(8*9*10)... = sigma x = 1 to infinity (6/(64x^4 - 20x^2 + 1))+3
My Calculus teacher didn’t explain these and we have a test with them on it today. Thanks for this guide it was easy to understand and now I feel like I understand it entirely.
@@divyanshsinghtariyal9485 Kid and can you even differentiate between a non-profit organisation and bunch of money sucking bastards and 11th and 12th grades aren't higher studies Lmao..
oh my god! index was the key word here, I couldn't understand this at all for the entirety of math class today but when watching this video my brain instantly connected the word index with a loop in java and I instantly understood the concept. Geez, it's funny how fast you can catch onto something once the right words are presented
IKR! I haven't even studied series (Well I have but not in depth at almost collage level) and now I feel 100% smarter than all students in my class. This guy is the best!
I added the second series in 10 seconds. The numbers can be paired off to sum 100 1 and 99, 2 and 98, etc. There are 49 pairs plus 50 plus 100 totaling 5050. This may be done for any series with any standard linear increment
This is so helpful. We use Prentice Hall textbooks at my school and they're basically worthless for explaining how to do problems. I've missed two days of Algebra 2 in a row and this video just brought me some hope. Thanks!
Salam, I am littely crying after watching this video..... trust me i have studied over 20 uears in colleges n unis but none had explained it so..... please keep tuting us all and maintain your contribution to develop humans.....
I'm sorry for being late, but If you're still interested, here's how it can be solved: Noticed the sequence 10 + 30 + 130 + 630 + 3130, when you subtract each number to the number before it, the increment of the sequence is: u1 = 10 u2= u1 +20 u3= u2 + 100 u4= u3 + 500 u5= u4 + 2500 ->Now, we have the sequence of 20, 100, 500, 2500 (just ignore the u1 or the "10" because it doesn't have the property of the sequence), we can write it down as 20.5^x (for x=0 to 3) Back to the original sequence, you can break it down as: 10 + (10 +20) + (10+ 20 +100) + (10 + 20 + 100 + 500) + (10 + 20 + 100 + 500 + 2500) 5.10 + 4.20 + 3.100 + 2.500 + 1.2500 (v1) (v2) (v3) (v4) (v5) See how it all come together? ->Now, we can craft the function For sigma (x=0 to 3), {the reason for this is we only take the sum from v2 to v5} we have ((3-x).(20.5^x)) Don't forget to bring back 5.10 (v1) to the sum as we have left it out. => 3930
@@17honhathong56 I really like the math in this reply, but I think the original comment was asking for a sum where 10, 30, 130, 630, and 3130 are the terms. I believe I have found such a sum, which I will share shortly.
Wow thankyou sm... I'm some one who has a lot of problems in maths but after seeing this i'm def done w sigma notation ....wow you guys should try ITS AMAZING
sir let me remind you something that you have forgot. there are people who cant't understand by the time your are doing your best but let me encourage you to the max please do you best to get those people in your box
Well, you could do a sigma notation where index i = 1, going to 10, and writing "2i" after the sigma symbol. That would add up all of the even numbers of 1 - 10.
In the most basic form of sigma notation, the index only goes up in increments of 1. However, you can achieve the sum you want by simply rewriting the expression. For example, say you have the sum from i=1 to 5 of i, like so: 1 + 2 + 3 + 4 + 5 But say you want increments of 2 instead: 1 + 3 + 5 + 7 + 9 You can do this by writing it as follows: the sum from i=1 to 5 of 2i-1. The "2" coefficient in front of the i is to ensure that our terms go up in increments of 2, and we subtract 1 to make sure that our first term stays the same, just like we wanted. If you truly want the index itself to go up by anything other than 1, it is possible. You start by defining a set, such as S = {1, 3, 5, 7, 9}. After that, you can declare that i ∈ S, meaning "i is an element of S". Then, the sum of all i, with the condition that i ∈ S (which we put under the sigma), is 1 + 3 + 5 + 7 + 9.
the formula tells you that. The index might not even be the value of i. It could be the index i of X and you have a list of arbitrary numbers out of order. So something like a list 5,17,3,and 20 the value of X at index i will refer to one of those numbers in the list. i = 2 is the value X= 17 in this case. There could be a formula that says, go up the index i in twos or threes, or whatever.
Yes, the index counts by ones from lowest to highest unless otherwise specified. The idea is that even if you want to count by tenths or tens, you would achieve that in the function by either dividing i by 10 or multiplying by 10. I suppose that constructing your own summations will be rare until college but by the time you need to construct them, you will want very badly to know how they work. Which is why I like your question. And why I'm here. Not really what I was looking for haha but I do like Sal's presentation and patience. Many college professors just ramble.
Wow this was absolutely awfully explained thanks! Way to go from using 1 and making it very simple to using pie and I squared. Definitely a genius way to confuse everyone!
The way you wrote the sigma symbol was chillingly perfection.
+Jessica I agree, he has nice sigmas.
Lol I can never draw it right.
Ligma ~ Sigma 😂
thanks to this video i finally understand Sugma meme
Jessica we are witnessing perfection.
Sooo.. it's basicly a FOR loop? Nice!
Finni M. programmers unite!!!
+Finni M. Code
+Finni M. Yup!
+Finni M. It's a for loot except you cannot control by what increment the loop's index increases by, it's always 1. However, if you don't use the index in the looped part, but a multiple of it, the porblem can easily be solved, like I did in a random pi calculation formula from pi = 3 + 4/(2*3*4) - 4/(4*5*6) + 4/(6*7*8) - 4/(8*9*10)... = sigma x = 1 to infinity (6/(64x^4 - 20x^2 + 1))+3
+RaZe Shot code is not life, the real life you should live is beyond your computer screen...
Why can't teachers explain things this clearly?! Thank you!
My Calculus teacher didn’t explain these and we have a test with them on it today. Thanks for this guide it was easy to understand and now I feel like I understand it entirely.
Same here but two years later...wish me luck bro
@@mrinfinity1217 all the best my g (soz for late wishes)
Have a test in 10 minutes, wish me luck
@@The_Cringe_Connoisseur did you pass?
When you search for the lesson you don't understand on RUclips and multiple videos come up but you choose to watch Khan Academy.
Potatsu no . unacademy is way better
Divyansh TM you’re here, aren’t you?
@@divyanshsinghtariyal9485 Lol its not even closer
Padhai Lelo! it is better if you are doing higher studies like me.Not 8th,9th or 10 th grade maths and physics like you
@@divyanshsinghtariyal9485 Kid and can you even differentiate between a non-profit organisation and bunch of money sucking bastards and 11th and 12th grades aren't higher studies Lmao..
oh my god! index was the key word here, I couldn't understand this at all for the entirety of math class today but when watching this video my brain instantly connected the word index with a loop in java and I instantly understood the concept. Geez, it's funny how fast you can catch onto something once the right words are presented
I learned more watching this video than a 1hr 40min tutorial I had yesterday. Thanks
IKR! I haven't even studied series (Well I have but not in depth at almost collage level) and now I feel 100% smarter than all students in my class. This guy is the best!
Khan Academy would legit make any math problem look super easy in their tutorials! 10/10👋🏼
float sum;
for(int i = 1; i
Thanks, these videos are saving my grades from the wrath of my crappy algebra 2 teacher.
what grade did you get?
I added the second series in 10 seconds. The numbers can be paired off to sum 100 1 and 99, 2 and 98, etc. There are 49 pairs plus 50 plus 100 totaling 5050. This may be done for any series with any standard linear increment
thx, that really helped!😊😊😊
wow. we have a gauss on out hands ladies and gentlemen.
Genius ;)
this method simplified is wht arithmetic progression indeed is
You're the man Sal!
this video has been very helpful. thank you
Is it weird that even though I use the website I still make sure to find and like the youtube video because its so amazing?
Perfect timing. Just learning this now
@andyr roopram No, only needed it to pass a midterm. Don't remember any of this tbh lol
@@iVince905 wow u r still alive
@@slouchysenpai1970 haha yes, I lost my life in uni but I resurrected
And then God said: "Let there be Math!"
Hey, Vsauce! Michael here; math is a tool that most professionals use, and it's a great thing that we discovered it.
Or did we?
*Vsauce music plays*
Teacher literally said to learn this part ourselves when we had 15 minutes of class left at the end.
makes it sound so easy!
This is so helpful. We use Prentice Hall textbooks at my school and they're basically worthless for explaining how to do problems. I've missed two days of Algebra 2 in a row and this video just brought me some hope. Thanks!
Same happened to me! Did you catch up?
Salam,
I am littely crying after watching this video..... trust me i have studied over 20 uears in colleges n unis but none had explained it so..... please keep tuting us all and maintain your contribution to develop humans.....
Thank you it’s very concise and helpful
Thanks for this wonderful explanation.
OMG!!!! U ARE GENIUS ^~^
one equation is (i(i+1))/2 for sigma notation
Thnx you so much I really understand
local count = 0
for i = 1, 100 do
count += 1
end
print(count)
count = 0
for i in range(1, 100):
count = count + i
print(str(count))
Umm, What the Sigma?
What is the sigma notation of 10 + 30 + 130 + 630 +3130?
I'm sorry for being late, but If you're still interested, here's how it can be solved:
Noticed the sequence 10 + 30 + 130 + 630 + 3130, when you subtract each number to the number before it, the increment of the sequence is:
u1 = 10
u2= u1 +20
u3= u2 + 100
u4= u3 + 500
u5= u4 + 2500
->Now, we have the sequence of 20, 100, 500, 2500 (just ignore the u1 or the "10" because it doesn't have the property of the sequence), we can write it down as 20.5^x (for x=0 to 3)
Back to the original sequence, you can break it down as:
10 + (10 +20) + (10+ 20 +100) + (10 + 20 + 100 + 500) + (10 + 20 + 100 + 500 + 2500)
5.10 + 4.20 + 3.100 + 2.500 + 1.2500
(v1) (v2) (v3) (v4) (v5)
See how it all come together?
->Now, we can craft the function
For sigma (x=0 to 3), {the reason for this is we only take the sum from v2 to v5}
we have ((3-x).(20.5^x))
Don't forget to bring back 5.10 (v1) to the sum as we have left it out.
=> 3930
@@17honhathong56 I really like the math in this reply, but I think the original comment was asking for a sum where 10, 30, 130, 630, and 3130 are the terms. I believe I have found such a sum, which I will share shortly.
Hey may I ask does the 'i' and 'n' represent the same thing? thanks in advance!
Yes
you just give the solution of the variable like in an equation
Wow thankyou sm... I'm some one who has a lot of problems in maths but after seeing this i'm def done w sigma notation ....wow you guys should try ITS AMAZING
Best academy for IT students thanks ...
your handwriting is so beautiful
Thanks for making this video. I see this sigma symbol all over Wikipedia, but I never knew what it meant until now.
Khan is credit to my know ledge!!!!!!!!
RUclips teaches me more than actual teachers. Idk whether it's good or bad 🤷
It's good for students, it's bad for teachers
6 years ago and still useful Thanks!
Real ( I’m Arabic)
froget all my alebra and never even took precalt, which are needed for uni stats. Thank you sir, the math aspect is all making sense
Oo oo😯 i don't believe that i will get my answer in 2 minutes
Oh my god this is awesome 🎉🎊🎆🎇🎍🎄🎄🎄🎖️🎖️🎊🎆🎇🎉
Awesome math teacher!
math is amazing
Is this kinda the math version of a while loop and incrementing a variable up to a certain threshold?
I think a for loop is a more fitting analogy.
we need to read it summation
Wow it's rely that simple
I don't even want to do mathematics as a career and I LOVE sigma notation
Extremely clear of the explanation, even better than my college teacher. BTW Love your voice
WOW, I didn't realise thanks!
Cool. So can you do stuff like multiplying at each iteration instead of adding?
That is done through capital pi notation, you can google that if youd like
Cameron Belt Cool. I wonder why it's called capital Pi, when that greek letter is already used?
Yep, its called capital pi notation, probably a whole different subject, but it exists
The Capital Pi means the product of a series, which you wanted. It follows the same method of being written out.
r u alive?
THXXXXXX
this instantly came to mind:
for(int i = 0;i < 100;i++)
this is really helpful! Thanks!
what a sigma!!!
That was the best explanation that I've ever seen. Thanks
THANK YOU SO MUCH NOW I'LL DO GOOD IN TOMORROWS EXAM.
Mytee how’d you do on your exams?
Great explaination.😄😄😄
Thanks you made sigma feel easy
I am 12 years old and I finished learning quantum physics, and learning calculus and topology in string theory 😊😊😊😊🌍🌍🌍🌍🌍🌍🌍
How and what are the resources ?
And yet you didn't knew about summation
Lmao. I'm 8 and got a phd Havard here. It's been pretty easy for me. You should go home and study more, we don't accept such failure.
sir let me remind you something that you have forgot. there are people who cant't understand by the time your are doing your best but let me encourage you to the max please do you best to get those people in your box
I just mastered it like a pro
Nice
Hi there I am amazed by the tutorial...
Thank you,i Will understand it easy-ly
Ahhhh this was a lifesaver. Tysm
This is good information! Thanks for explaining.
Wonderfully explained Siir ❤
thayynk uuuuuuuuuu sooooooo much sir.....
Sigma Mindset
bru
Thank you Khan!
Is there any way to increment "i" by any number other than 1 ? (Using Sigma Notation)
Well, you could do a sigma notation where index i = 1, going to 10, and writing "2i" after the sigma symbol. That would add up all of the even numbers of 1 - 10.
In the most basic form of sigma notation, the index only goes up in increments of 1. However, you can achieve the sum you want by simply rewriting the expression. For example, say you have the sum from i=1 to 5 of i, like so:
1 + 2 + 3 + 4 + 5
But say you want increments of 2 instead:
1 + 3 + 5 + 7 + 9
You can do this by writing it as follows: the sum from i=1 to 5 of 2i-1. The "2" coefficient in front of the i is to ensure that our terms go up in increments of 2, and we subtract 1 to make sure that our first term stays the same, just like we wanted.
If you truly want the index itself to go up by anything other than 1, it is possible. You start by defining a set, such as S = {1, 3, 5, 7, 9}. After that, you can declare that i ∈ S, meaning "i is an element of S". Then, the sum of all i, with the condition that i ∈ S (which we put under the sigma), is 1 + 3 + 5 + 7 + 9.
@@phoenixroyaleYou mean the even numbers from 2 to 20.
@@isavenewspapers8890 thank you, 3 yrs lol
@@Pa1_Thakur You're welcome.
Best explanation ... Thanku sir 😀
I could meditate to this
it's called "for loop" in programming.
were you not supposed to end at 49 as 50 is the position of the last number and you started with 0?
eben kaale the goal is to reach that increment in the index, not create an index based on that value.
How do you know what increment it is increased by? Is it always the value given by the index?
the formula tells you that. The index might not even be the value of i. It could be the index i of X and you have a list of arbitrary numbers out of order. So something like a list 5,17,3,and 20 the value of X at index i will refer to one of those numbers in the list. i = 2 is the value X= 17 in this case. There could be a formula that says, go up the index i in twos or threes, or whatever.
Yes, the index counts by ones from lowest to highest unless otherwise specified. The idea is that even if you want to count by tenths or tens, you would achieve that in the function by either dividing i by 10 or multiplying by 10. I suppose that constructing your own summations will be rare until college but by the time you need to construct them, you will want very badly to know how they work. Which is why I like your question. And why I'm here. Not really what I was looking for haha but I do like Sal's presentation and patience. Many college professors just ramble.
Basically factorial but addition
I rather pay u than my bloody tuition😂
🤨🙂👉
Thank you!
2:00 ok
So lets use n
100
Σ n
n = 1
Like this right
For loop moment
thanks
How do you do it if you don't want to increase by 1
multiply the index.
thx alot it helps me actually I'm grade 7 but I skip grade
This man don't Forcha
I somehow made it into the second year of a computer science-engineering degree without knowing this
Thank u sir ☺️
Nice method
Was wondering how th this worked after getting out of work.
does it mean the first sequence starts like: (1+1)+(1+2)+(1+3)+(1+4)+(1+5)... instead of starting by 1?
can the index be in decimals?
I am one giant enigma!
God he has the sexiest voice!
fun u
Really? I just found it to be too American
lol
He does!!! Very calming, and explains better than my Professor..!
Yeah..
Do you know Salaman Khan is founder of Khan academy Thanks so much sir....
this is really basic information, it's to late cause my exam is tomorrow.
thanks anyway Sal !
+The Chosen One How did the exam go?
+Learn Maths Free i passed it with B grade :)
+The Chosen One
good job even though it's not A but it's still good good work buddy :-)
thank you
What is sum when k takes values from 1 to n, of K! * K ?
Sigma. reminds me of something
Thank you, this really helped me get a good sense of the sigma notation for sums.
Just do this (x+1)x/2 it works sometimes.
Cringy 7-Year-Old that only works for a natural number sequence lol
keyboardmannow, “It only works *S O M E T I M E S .* “
Cringy 7-Year-Old i acknowledge that, I was just stating that for other people who look
Wow this was absolutely awfully explained thanks! Way to go from using 1 and making it very simple to using pie and I squared. Definitely a genius way to confuse everyone!
It’s a for-in loop 😀
hello i am from VN and i'm learning math in english and i have sth to ask
How to read the notation of Sigma
"sum from [index] equals [bottom number] to [top number] of [expression being summed]"