Sequences and Series (part 1)

[ananyakirti]

Nice!!

Although the last step has a mistake

[acm22fan]

how is this guy so smart?

[Odeferous]

How many are there?, There are N of these. LOL good video.

[CaptainSuspenders]

This was a life saver. I go to an online school, and the way they teach math is a little.. iffy. It's very difficult to learn, and I was starting to lose faith in my own intellect. Thank you for restoring it. :]

[Y01AndAyIp]

i can't even hear ur burp in there though

[inezraharjo]

LOL I was distracted when he somehow keeps on clicking 'clear images' over and over again..

[XxNovaflyxX]

I was wondering, do you give the Fibonacci sequence (1,1,2,3,5,8,13,21...). If you do can you give me the link to the video, if not, can you make one?

[ConquistadorAlfred]

wait, the [n(n+1)]/2 is only if the number starts at 1 and increases by 1?

[Tupacbldz]

If the nth term of a sequence is 6n-1, by how much is its 40th term greater than its 28th term? can some one help mee ? plaseee i dont really get et this is new to mee n i need to know this for myy sat

[tedoymisojos]

I didnt understood how you got at th eformula at all:S but I get how to use it

[oxspy]

The government should pay you instead of my teacher :)

[Wandelaarke]

Thank you :)

[tyhilldaman]

OMG! The ingenuity behind series astounds me! I think that's so freakin' cool that someone came up with this!

[nitrorev386]

hey Sal, can you do some vids on the other convergence tests in depth. Integral test, telescoping series, nth term root test, lim comparison test etc. thanks.

[itechkid]

damn this was before Sal was a premier partner – he still had the 10 min video limit...

excellent as always, mate

[ACfireandiceDC]

Sal is too confusing and slow for me and 13 other people

[itechkid]

@ACfireandiceDC You and 13 other people need to get back to basics.

[ACfireandiceDC]

@itechkid apparently, these ARE the basics.

[itechkid]

@ACfireandiceDC There's always the fundamental basics.

[Zander101084]

sophomore year of algebra two.... in 9 minutes!

[LikidySplitz]

If this is too presumptious, God help you. Thank you khan, you saved my life again

[FlyWithMe4ever]

that awkward moment when I've learned more from a 10 minute youtube video than from my precalc teacher who I've had all year.

[kisasohma9]

@FlyWithMe4ever Are you referring to nigahiga? The awkward moment when you say goodbye but you walk in the same direction. That has totally happened to me before, lol.

Thumbs if you either watch nigahiga videos or had that happen before-where you walk in the same direction after saying good bye

[pimpmymail]

I am loving you :) got a calculus exam tomorrow and I SHOULD study everything from khanacademy.... Thanks

[MarkyJayStudios]

holy crap your good at drawing with a mouse

[guitaringjarmin]

@MarkyJayStudios Sorry to burst your bubble mate but he uses a interactive pad

[MarkyJayStudios]

@guitaringjarmin haha i know i was kidding...

[dillonjbritt]

@MarkyJayStudios i dont think its a mouse

[averyshikanai]

haha, nice series pun at 8:04

[JananaXD]

i dont know why but i think you are hilarious, you are my only hope to passing math class.

[juuustmee]

sal you are great! you're totally saving me x)

you should do videos for multivariable-calculus aswell because I don't understand a thing of it :s

[barnamah]

at 1:34 and 2:30 has say (N-1). Where is he getting that from? he failed to explain that thinking that we know it. Well we don't. We expect it should be N+1 because it is increasing.

Can Mr. Khan explain it to me?

Thankyou

[GnihtonchloE]

@barnamah well since 1,2,3...N is in an increasing trend, the item before N should be 1 less than N, which is N-1. Just like the item before 3 is 3-1=2. Since we want this sequence ends up at N, then N+1 which is 1 bigger than N, will just exceed the range we want.

[enjoyablesounds]

As of last week I started studying "sequences and series". Again, the branding chosen inappropriate and unnecessarily confusing , not distinguishable at all. I would leave "sequences" as it is but would refer to "series" as "add-series" or better yet "add-sequence or sum-sequence" simply because now, in the word the clue of summation already has been giving in the initial descriptive sense. what do you think?

[watdafact2]

try casing that cursor with your own!

[88fierogtp]

A long long time ago, some poor bastard spent a lot of time thinking the shit out of this. Hot damn.

[everlastingauraX]

Why do you put (N-1)+N at the end?

[missbassoon1992]

@everlastingauraX because when you reach the last number in the sequence, N, N represents the last number in the sequences, and N-1 coming before N is simply the number before N. hope this helped

[carlosav]

This is a great trick, but it only works if you're taking the sum of a sequence of positive integers with one as its starting point. There is a more general formula for finding the sum of all the integers between any two positive integers a and b (b > a) : (a+b)(b-a+1)/2

[LucyRockprincess]

omg i still don't get it.. i feel like a dumas... :( ughh someone help me

[1073601]

thanks for the proof

i've always been wondering why the sums of N is n(n+1) / 2

[divinedejesus25]

nice handwriting



[Hellsslave666]

@abombinreverse Do you need glases?

[naughtydevil02]

that is so awesome!!!:)

[hedonism13]

Now I'm a magician!

@sajidullah

Buzzkill of my excitement.

[golliwogschen]

Clear Image!

[sajidullah]

These tidbits of knowledge, as we have abused,will become the cause of our destruction..A knife can be used to cut a cucumber or stab a human being...u know what ia mhinting at?

[metaltuned]

@sajidullah no we dont!

[rayz3678]

This for core 1 a-level?

[leonharts]

What's up with N-1 then the next term being just N?

[scikud]

hey i have a question~

why are we adding the sequence in reverse.. i mean i understand its function but why intuitively would we add this reverse sequence to the original

[daengbo]

This may be covered somewhere in the seven pages of comments, but I don't want to read through all of them to check. Anyway, I want to assure you that your gut is right: arithmetic has stress on the first (minor) and third (major) syllables when it's an adjective (an A-rith-ME-tic series) and second (major) and fourth (minor) syllables when it's a noun (Let's .study a-RITH-me-TIC). The pronunciation of the vowels changes, with the unstressed vowels being reduced.

[phiphers]

i demand u present a video demostrating the sum is wut u say it is !! :P

[madscirat]

What math textbooks fail to explain in ten pages of proofs, Sal explains in two minutes of common sense. Thank you so much, I no longer fear summations.

[thill202]

Just wondering do you have any videos involving fourier series

[BooganaMonkey]

OMG !! THANK YOU SO MUCH !!!! i hated sequences ... not that i still dont but then its not that bad xD <3

[onlyAerik]

Why is these 2 videos listed after the solid of revolution videos in the calculus section? I would've put these at the end of the precalculus series so we can have a better intution about summing infinite numbers of infinitely small changes (dx)

[lonogugeadult]

"That would have taken you forever to do that!" lol

[picarolus]

I love you!!!! You are helping me so much :)

[annarosco]

weak

[crodd63]

i do think that at the end of the video, (Geometric) it's not supposed to be a^(n-1) + a^(n-2), i think its supposed to be a^(n-1) + a^(n)

[g1code]

the mistake is already corrected in the next vid

[KeyOfAm]

@crodd63

Does make sense, I dont really get why it goes a^n-1 , a^n-2

[winstonfc]

@KeyOfAm Because it is n terms. The theorem must show arbitrary values that are not raw values. Just like when he showed 1, 2, 3, 4,..... (n-2), (n-1), n. Just switch the numbers for a and raise them to the power of the same number.

[winstonfc]

@winstonfc Although now I see the mistake he made ^^

[trongtan84]

burp :)

[InnocentxR]

why do you have to add the (n-1)+1?? i really don't get sequences and series. . .

[lucile1010]

@InnocentxR I think, I think he's trying to show us where d formulae come from?x

[Vengetic]

@InnocentxR He's just giving it as an example, instead of just going to N say for example N is 100, he's saying N-1 + N which will be 99 + 100 he can do this because the sequence is increasing by 1 everytime.

[waleedgilani]

why did you add sigma k???

[DanielKovach]

I am very excited about the 1, 2, 3, 4 sequence!

[ponit54]

Or you could multiply 101*50 because theres 50 numbers to the left and 51 to the right to get 5056.

[weka]

The last example. Shouldn't it be a to the (n-1) and a to the (n) rather than a to the (n-1) and a to the (n-2) as he has it? That's what his notation says.

[Thymonico]

"The most difficult sequence is: 1, 2, 3, ..."

?? I learned that when I was like 3!

Is it "difficult" he's saying there?

[david887]

No, I thought that too, but when I went back to it I realized that he actually said "The most typical sequence..."

[Akrubix]

@Thymonico

I think he say's "typical", not "difficult". :)

[alexPsanz]

im not done but im getting the feelin my mind is about to get blown.

[maksman93]

number before N, could be anything, dont worry about it ;)

[Anikaangellove]

Why do you do N-1 ? Just lost me at those points.

[DTNRom88]

N-1 being the last point before N. For example if you're counting up to 5 you would go 1,2,3,4,5.

if you replace 5 by "N", then what would be the theoretical value of 4? It's N-1 (5-1 = 4)

Basically N-1 is just a way to say the before last number in your sequence

[DesertedBaby]

it think its a representation of what each value in the sequence would be

e.g the first value would be (1-1) +1= 1

second (2-1) +1= 2

third (3-1)+1=3

1,2,3.... etc

[kamyarghofrani]

cuz they are in order, if the last number is N, the second last one is N-1

[maksman93]

N-1 is the number before N. so if N would be 9 then he would write: "1+2+3....+8+9"

dont worry about it, he did it to represent that number nothing more ;)

[nickrohn93]

@maksman93 thank you

[ose90]

the N-2 should be N... thanks sal!

[chrypton1]

@ose90 Was just about to comment on the same thing :P

[TheFrycry]

Graet video! sal thanks!

[bilvol]

Thanks Khan, you have demystified another math snob concept.

[Ritzoid]

Burp, belch, or fart, this was way better than reading the convoluted explanations in my textbook. Thanks a trillion!

[jhonma1]

Thank you Khan.

[Acolyte14]

Holy, you're fast with the mouse when writing LMAO

[1Mperios]

lol I think he uses a graphics tablet : D , if not then yes he is : )

[Hyubussa1]

the terms he circled look like dicks!

[donlu0980]

9:13 isn't the last value of a should be a to the power of N ? why u wrote N-1 then N-2 ?

[Jlangbridge07]

yep its spose to be ...a(n-1) a(n).

Brackets for powers :)

[huge1234]

no because its geometric, the powers are the same as (n-1). If you notice the 1st term is to the power of 0 and the second term to the power of 1 etc..

[JayQuebec116]

NO! (n-2) isn't ( (n-1) + 1 )

[zackmoya507]

how would you solve it if it had sides of both geometric and arithmetic series

its asking for the sum of the sequence 1 through 51 and the equation is (3k+3)

I can't figure out how to answer it through either of these videos

[pipbeard]

I am taking Higher Level Maths on the IB course, and your video's have been a huge help and your style of teaching is exceptional. I have my second maths exam 2moro and i feel like i may just pass it!

Just wish i found you earlier!!! Thankyou

[GunDream]

Khan is a good teacher. My teacher is a caltech Phd, but it took him 20 minutes to explain this concept.

[Beefstew2011]

Pure ownage.

[lawsonfulton]

Are you implying Sal does not exist on Earth?

[ruitye75ir94444]

A whole "series" of scientific... this shows up a lot.

Punny!

[GDATERRY]

Thank you so much for expaining. My teacher just randomly started writing these formulas without saying anything and everyone was just sitting there. We could work out what he asked us by following his examples and replacing numbers but we had no idea what the reasoning behind it was. Heck, I didn't even know it was series and sequences.... >.> (and trust me, I was paying attention real hard, and other people in my class couldn't explain it either and said they needed to consult their text book)

[PianoWallaby]

This one belongs on your greatest hits.

[toknowthetruthofgod]

Thank you! Now, finally some hope for me in Math (maybe). God bless you!

[hellocinnamon]

Wow!! This is amazing. Thank you!

[machvis]

thanks great video!

[its123baby]

I loved the burp!!!

[gramatikov]

errr, don't you have to write the rate in the sigma notation?

[Max11551]

I think at the end of the video there is a mistake. You say the last elements of the series are a^(N-1) and a^(N-2), but shouldn't that last one have been a^N ?

[khanacademy]

You're right. I fix them in the next video.

[Max11551]

Yeah, I found that out just a minute after posting the comment. :) Sorry about that.

[brco2003]

But it looks like he crosses out the '-2' on the top line.

[anvilsalesman]

woah, nice video. thanks a lot, I'm using these to teach me the C part of the BC calc AP.

[Nandine2]

khan is king!!!