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Sigma notation for sums | Sequences, series and induction | Precalculus | Khan Academy

1 036 765 views | 8 Nov. 2013

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Watch the next lesson: https://www.khanacademy.org/math/precalculus/seq_induction/geometric-sequence-series/v/geometric-series-introduction?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus

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Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!

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Wander Lust


Shawn Yama

It's funny that they they never teach this in school like they just expect you to know it.

Admin Iraneconomic

I am back here again, I dont use sigmas enough to hold them in my memory

Zack E

How do you do it if you don't want to increase by 1

JBW ___

Who else here is 14?


is summation notation and sigma notation the same thing?


I learned more watching this video than a 1hr 40min tutorial I had yesterday. Thanks


Agh it reminds me of Java

Aditya Bagaskara

So it's a factorial but it's in addition


Thank you Khan!

Dulce De Los Santos

This is good information! Thanks for explaining.

Not Jared

6 years ago and still useful Thanks!


And then God said: "Let there be Math!"


oh basically substitution ?I thought it was something different

Crystal Cleared

Eww i for index

Mercury Reborn


Aniket Jaiswal

Great explaination.???

Dylan Evans

is writing (i=) redundant? can you just put 1 and 10? do people sometimes retain the i?

Kartik Agarwal

I just mastered it like a pro

Smart Science

I am 12 years old and I finished learning quantum physics, and learning calculus and topology in string theory ???????????


How do you know what increment it is increased by? Is it always the value given by the index?

Ria Legara


Iron CYR

math is amazing


As a programmer this is extremely trivial


"mathematical career" no i'm just trying to graduate high school... i'm never gonna use this again XD

Kritika Kumeri

Best explanation ... Thanku sir ?


What is the sigma notation of 10 + 30 + 130 + 630 +3130?

Ben Dauber

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?

Carlos Marquez

What’s sigma

Muscle Man

Khan Academy would legit make any math problem look super easy in their tutorials! 10/10??

Nea Jullana

How do i write the summation notation of sum of the first 10 terms in 27,24,21??



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.....


Online school got me here


Ahhhh this was a lifesaver. Tysm


does it mean the first sequence starts like: (1+1)+(1+2)+(1+3)+(1+4)+(1+5)... instead of starting by 1?


0+1+2+3+4+5+6+7+8+9+10, n=11
Sn= 11/2 (0+10)
Sn= 5.5(10)
Sn= 55
1+2+3+4+5+6+7+8+9+10, n=10
Sn= 10/2(1+10)

Pawan Thakur

Is there any way to increment "i" by any number other than 1 ? (Using Sigma Notation)


Oh my god this is awesome ?????????️?️????

1103 Musik Berlin

Your Track is great, i hope you listen my songs https://www.youtube.com/watch?v=g_7jkntnNZk

zuhaib asad

can the index be in decimals?

Awais Food point

Nice method


Well explained well done bravo

Parasuram Rajesh

we need to read it summation

Aregbesola Debo

It was this simple (◎0◎)ᵎᵎᵎ

iX Relaxx

Yeah but how do you do it without writing all the 50 terms out? Come on now.

Chanuth Gunawardene

WOW, I didn't realise thanks!

TheAmazing Jon

Was wondering how th this worked after getting out of work.


Basically factorial but addition

daxtron max

Thank you,i Will understand it easy-ly

eben kaale

were you not supposed to end at 49 as 50 is the position of the last number and you started with 0?


your handwriting is so beautiful


Any korean?

Baljit Singh


gabi lovesinging

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

Ken Law

Extremely clear of the explanation, even better than my college teacher. BTW Love your voice


What is that melody

Crack Head


Melissa Patton

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!



Bhat Majeed

thayynk uuuuuuuuuu sooooooo much sir.....

316 Monis Bandey

really hard to see anything



NA Sound

thank you



박 지민Park Jimin

Sigma balls


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

odb 1997

makes it sound so easy!

Abdullah Alkharji

so what is the sum of the the name that you wrote

Saanvi Mitra

YouTube teaches me more than actual teachers. Idk whether it's good or bad ?

Johnanthony Bernabe

Whos here for mr beasts riddle?

Junior Cooper

Not helpful




Why use i for index? i is taken already, that's confusing.


When you search for the lesson you don't understand on YouTube and multiple videos come up but you choose to watch Khan Academy.

Colin Whitlock

Teacher literally said to learn this part ourselves when we had 15 minutes of class left at the end.

Thor Stambaugh

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

Halilintar Hardani

Please, add the indonesian subtitle

Aman Chopra Motivation

Do you know Salaman Khan is founder of Khan academy Thanks so much sir....

Nik Pipa

You sigma notation and writing is better then my notebook writing.

Yaquan Liang

Hey may I ask does the 'i' and 'n' represent the same thing? thanks in advance!

Glo Bo

is there a formula for this in Excel? other than =SUM

Harry Blackwood



How do u pronounce that i need it reply asap

James Richardson

So, I have a large problem I want to solve. I am trying to find the circumference of an ellipse. I found a formula that is below

C=π(a+b)Σ(.5/n)^2 *h^n

Is this formula correct, If so, how do I solve for an infinite sigma?

Jeff Mutt

Hi there I am amazed by the tutorial...

TF2 Soldier

Time to challenge the smart kid in my class.

Melan 6BITS

Best academy for IT students thanks ...


What is the meaning of the i which is to the right of the sigma ?

Petrish Legaspi

What if the I starts at 6? Fck Math

Giorno Giovanna



What is that melody?


I rather pay u than my bloody tuition?


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.

Suyash LoneWolf

What a useless thing it is

Paige G

who else is studying for FINALS?


no way to change the incrementor? dangit :c

Mr. Blue Notes

So basically what you're saying is that, using this method, we can shorten the patterns using this?

Habib Khan

Oo oo? i don't believe that i will get my answer in 2 minutes


How do you write so beautifully with a mouse

Cringy 7-Year-Old

Just do this (x+1)x/2 it works sometimes.

Notation capital

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D and L configuration

14 132 views | 10 Jul. 2020

How can we assign D and L

How can we assign D and L configuration for both Fischer projection and wedge & dash line projection. So in this video we will see what is D and L notation, how can we assign this configuration to carbohydrates and amino acids. We will also discuss why this is known as relative configuration and what is its role in series of carbohydrates.



Aryan Kumar gupta

Thanks a lot

Pravin Amrutakar

In bahal and bahal book their is mentioned in fisher projection group on horizontal bonds come towards the viewer and on vertical away from the viewer it is opposite as u say. Pls check it .


Which is more predominant? L or D?

Kotaru Kumari

While converting from wedge dash to fisher projection u said that if group is on right put it on left in fisher projection and if we do that vertical line groups are coming front and horizontal are going back

World of easy maths

Good explanation
Keep it up bro
Wish you a great success
Thankyou for making the vedio

ShYaM JaDhaV

Sir horizontal lines are above the plana a/c to fisher proj, u did mistake at 2.19,in previous vid u said that ,the horizontal line indicates grp above plane , in this vid u said horizontal grp are below

Taha Şahin

student: I dont understand
teacher: WelL yoU are stUpiD!!!!!

that man in the youtube: I will teach you my son

thanks for the video ♥

multi action moviez

Good teaching

animal lover in tamil


Naanthaapa manoj


Unnati Uniyal

Tq sir

Susheela. S.Korishettar

Tq Sir,ur teaching is really excellent.

Job Ombaso


Gargi Das

First view

Gourav gaming

Wow good content nd explanation. I really got the topic

World of easy maths

I have an idea to improve your channel

Last 5 min
Try to give some examples to us
Say to keep the answers in comments

Notation capital

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Model notation (STAT 320, week 2 video 1 of 6)

161 views | 13 Sep. 2020

Introducing the Choose Fit

Introducing the Choose Fit Assess Use framework, general model notation.

Goran Adil

Dear Amelia, which book you use as a reference? and thanks for sharing these videos. do you plan to share rest of the course?


Loving the channel. Keep it up! Why aren’t you using smzeus”dot”com!!? It’s the best way to grow your channel.