What is a Sequence? Basic Sequence Info

[akukurt1]

hey, please fix your paypal donation link.. i owe you a lot..

[patrickJMT]

@akukurt1 it seems to not work for people in certain countries... otherwise a couple of people sent me $5 the other day, so it should be working : )

[lindap2012]

an excited 5! lol



[hadeel1987]

i love you!

[albssam]

Thank you.

[missbackoff]

i love the way one sounds coming from his mouth

[patrickJMT]

@missbackoff lol

[missbackoff]

@patrickJMT your the best teacher i have every had 

[patrickJMT]

@missbackoff : )

[lordkhalloody]

hello patrickJMT i get 2 from 20 degrees in my first exam in calcullus 2 (intigrations and secuenses) how can i succed in this term its remain 80 degrees and the succeed mark her 60 from 100 can u help me wt shall i do in this maths?

[crazydom117]

Lol magic math in the wonderful world of MathNarnia (:

[ahmedpharoah]

please by my private tutor i will pay you 100 k gold

[reddevil16carrick]

Hey Patrick, You should use Twitter. Not for us to ask you math questions but to interact with you because I think it's safe to say we are all(besides those idiotic 14 people) sort of your fans now

[patrickJMT]

@reddevil16carrick ha i will consider it. i had a facebook page with about 1400 friends but i deleted it! : )

[FERViolin2010]

@patrickJMT you cant really delete facebook if u log on watch u get all ur info back as if nothing happen

[patrickJMT]

@FERViolin2010 yes, that is why i put nothing personal on there. i will never go back to that site

[ShrodingersPerson]

nevermind i figured it out. Note the minutes of delay between question and figuring it out. yea Im sooooooo smart. -__-

[ShrodingersPerson]

I got a quesiton....Why does the lim n->inf. (2/3)^n equal 0? Can you answer soon please? Thank you, and much respect for what you do.

[075jpark]

what are you saying the final answer is?

is it 0 or 1/3?

[TheMadSlick]

@075jpark He made a mistake. 1/3 x 0 = 0. The final answer is 0.

[xplorsonu]

patrickJMT = favourite brand

[patrickJMT]

@xplorsonu ha, i guess i sort of am turning into a brand. weird to think about...

[xplorsonu]

@patrickJMT So highly honoured to receive such an instant reply from you, indeed. I am full of praises for you in my mind every time I finish watching your video but I refrain from writing it out here. I am a proud fan of yours Mr.Patrick,the reluctant hero.

[macabrebunny]

@patrickJMT Are there t-shirts?

[Jennbaybeeful]

Ughhh , I have A Test On This Tomorrow ! :( FML

[Shabontiac]

1234 videos .. sequence :D

[coolboyshubham]

MatHz star ......

[wizardval]

Thanks bro. I love you, no homo!

[weirdandshort]

your videos are lifesavers my professor cannot teach at all so thanks a lot!!! finally someone who actually knows how to teach people math

[snozzla]

Thanks!

[sano0311]

You should start selling CD's....."learn math in 30 days or I will give your money back"

[EastSidePaul]

Hey is there any chance you could give a tutorial on when a sequence is graphic in Graph theory, and also the Prufer sequence?

[ConstantineRobbins]

LOL

[princessazula]

Let me just tell you that you have been my professor this year. Thanks so much for everything! My professor could DEFINITELY use some lessons from you! :/

[mamatela]

mmmm nice harry hands papi!

[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?

[patrickJMT]

@enjoyablesounds i think i am not sure what you are saying

[edde8282]

Great video! you are always spot on with the explanations. Q: Just have one question, when you separated the denominator into two 3^1 times 3^n, how is it that it does not changing the problem to 9^n if you where to pice it back together?

[Nandinho239]

@edde8282 the 3 does the job of an X? for example x^n * x^1 = x^n+1. Got the idea.

[lilangel0072]

LOL! math magic hahahaha 

[Johannady]

wow.. you even have a sequences tutorial... :p Thank you ^^

[patrickJMT]

@Johannady lots of sequence and series stuff

[iMysteryTube]

nice weiting

[lizziedoll456]

It just dawned on me that you're left handed too.

WHY ARENT WE BEST FRIENDS?

[mirrin55]

...I think this is the first math lesson I actually enjoyed...

[NeVarajMe]

"wooone, point wooone, point zeerow wooone, point zeeerow zeeerow wooone.." lol at ur accent.

[ALEXRUNSREACH]

Dude, you're a better teacher than my actual teacher lol!

I actually paid attention to the whole video and none of it was confusing.

[star7girl]

oh i sooo WANT to learn new stuff, and i know these but the way you explain doesn't make it boring at all. i wish i had you as my teacher. we had a curriculum change and even if i am in AP i have to sit in class and listen to the same damn thing i learned last year. argh i hate my life! i mean math is like the best thing and i love it to death and i want to learn new things but noo stupid public school system!!! lol i do sound very nerdy. but that's ok :)

[patrickJMT]

@star7girl nerdy is just fine : )

i had a less than stellar school experience too; that is how it goes sometimes.

do not let that stop you: read and teach yourself!! that is the secret to learning.

[star7girl]

@patrickJMT yes that is why your videos are great for me to learn further. keep it up!

[Ashenfly]

too high to watch video..

Enjoying the nerdy math comments though. Not in a mean way..

If i was as smart as that id bragg too

[patrickJMT]

@Ashenfly i was probably baked when i made the video

[Brettvella1984]

hmm, pretty sure the answer was 42, Good try tho, thanks for the video

[nassah2010]

its good to see that even good mathmetitians make easy mistakes just shows we are human :P.

thanks patrick

[2icebaked]

Holy cow, I wish this guy had been my math teacher.....

[archiemedes42]

All the converging ones converge to 0. Can't a sequence ever converge to a non-zero number? Or are they also like series and can converge to any number.

[cutedanzr4]

you are my hero

[krogan92]

So is a sequence approaching negative infinity still considered a diverging sequence? (e.g: 1, 0, -1, -2, -3,....)

[patrickJMT]

@krogan92 yes, this is divergent

[nathanialmunir]

thanx man thts realy helpful

[VAZNH]

this is amazing

[daham1989]

awesome man! r u a student too?

[ShivMan007]

hahha i love the magic math part

[jwmcmac]

the other mistake on this video is a small one . . . that you placed the ratio as . . .

. . . between -1 and 1 . . . but you used less-than-or-equal to one instead of just less than one. You were correct on the -1 side of the ratio.

I'm sure that you properly explain this somewhere along the way . . . as you always do.

Thanks! . . . and GOD Bless you for all of these wonderful videos.

[patrickJMT]

@jwmcmac a geometric sequence does converge if the ratio if -1 < r <= 1,

so what i did is correct. however, for a geometric SERIES to converge, the ratio must be: - 1 < r < 1

[Drkdominatordom]

to infinity and beyond !

[jayorca]

Please can you show how you will find the lim as n -> infinity of 3(-1)^n / n!

[VisualDesignFX]

im 13 years old and what is this?

[poroporoa]

Is Fibonacci a sequence ?

[vkcelik]

@poroporoa no serie

[patrickJMT]

@poroporoa yes

[Dethclops7]

@patrickJMT Thanks fir teaching us

[KOGR11]

good video 

[Aman1238]

What if a sequence increases by 5%?

[patrickJMT]

@Aman1238 then you have a geometric sequence.

[Aman1238]

@patrickJMT I knew that but I wanted to know how to get the formula. But nevermind now, I figured it out :)

a1 * 1.05^n-1

Thanks anyway :P

[alrasw]

i just started this topic this semester and im so excited...im learning what im yet to learn...i really appreciate that u share ur knowledge....freely...lol

[alrasw]

i love u soo much!!!

[Sikmind08]

who wouldn't love math if they understood it.

[granadaza]

Patrick can you tell me why 0! is 1?

[patrickJMT]

@granadaza well, it is 'by definition' - otherwise, many statements about factorials would not work and one would need a special case. factorials are also used to count arrangements where order matters, so i have heard some say: how many ways can you arrange zero things: in ONE way, that is, not at all. personally, i do not find this that satisfying. to me, it is a needed to rule to make many formulas and statements correct. we can define as we wish, so long as we are consistent after that!

[archiemedes42]

@patrickJMT Well, why do you say it isn't very satisfying. Ignoring the n!=n(n-1)! dodgy proofs, there has to be 1 way to have 0 cards in a row. Otherwise, if there are no ways to have 0 cards in a row, you couldn't possibly have 0 cards, meaning you'd always have to have at least 1 card with you, even in the tub :P

[jastinhaha2]

thankx man

[princekashyp]

hey man ur doing great job here u explane vary well every thing thax sir its great

[yondaime500]

In US when you write a number such as .1, you don't write the zero before the point cause it would be a leading zero right? In Brazil we write it 0,1 (yes, with a comma).

[patrickJMT]

@yondaime500 some people use the zero. i am too lazy to write it

[kevmcc7]

Infinity cannot be multiplied by infinity though right?

[SInnerMario]

man i got pissed about the answer beein 1/3 , am just learnin this and was like WTF i thought it should be 0 , now i dont get it , glad u corrected it lol

[babefreaktion]

@ EmilyShoutsILY: Same here! I would like to just pin point out the fact that you, PatrickJMT, are a lefty. And lefties, particularly among most who are men, are freakin good in math. I don't want to get into further details so that is all I have to say. But then again, I'm not saying that females aren't capable of math either. I guess it was just coincidence for me to find this vid.

[dfts22e]

Your videos are great, but some are hard to hear your voice. 

[jmbishop511]

lolsimplemath

Why was this related to a computer case video???

[EmilyShoutsILY]

I hate Math D: lmfao. you're smart though :D

[patrickJMT]

@EmilyShoutsILY sorry u do not like math - i did not really appreciate it myself for a long time - and i am not so smart honestly, but i am not totally clueless either

[elbarracon]

wow, this is related in a meekakitty video

magic tricks with math? xD

this remindme my school (the magic math too)

in my school there is a joke of those who those who attend a "factorial" semester

zero multiplied by anything is like... a chuck norris kick

well this is a bad joke but....

for suscribing i get math and english classes xD

[Akaecius]

I want you as my tutor ;-;.

[W11BO1]

I'm glad I only have to have another math credit to be done with math all together in school.

[emailwiz2]

why aren't you a teacher?

[patrickJMT]

@emailwiz2 i sort of am

[dashtucker]

Thank you for your videos, You've explained it nicely and its written out. (I like the magic math at the end :P )

[TheSiSiDreamz]

84% understood maybe ill watch it again lol

[mzhannah11]

i explain things very clear! keep it up

[sexy19081995]

fuck i hate sequences

[ThighDeepinTofu13]

psshh eeeeasy

[00JosefK]

@007sofian

Learn math, then go get an engineering degree...Or sell dope like my cousin ( he can give you some pointers in 3-5 years)

[007sofian]

@00JosefK thanx for replay

i have more than engineering degree and more than 4 years of graduation after (u and m, we are not from the same country )..

u have seen my opinion from one side.. i respect persons who get learning bay anyway. But, in our days, to have money u should tack another way.

[patrickJMT]

@007sofian you can pimp yo self out , lots of dirty old men would love you i am sure

[007sofian]

@patrickJMT Before you learn what is sequences you should learn how to speak with the others respectably.

[Millsie18]

@007sofian Lol.

[go4it7arh]

@5LiMxxShady I'm in 8th grade, an I know how to spell grade, unlike you.

[09458]

apparently, you dont know how to spell 'and'.

[go4it7arh]

@09458 Or maybe I typoed.

[jwk891]

@5LiMxxShady  and apparently you can spell as well

[mrlise]

I would just like to mention that for the first example you did on the page "convering or diverging," when you took the function (n(n-1)) and took the limit, it should go to +1 not infinite. This is because if you expand (n(n-1)) out and then divide both by n squared, you will get (1 - 1/n^2). Therefore as you take the limit of this, you will get (1-0) = +1

[jfoolin]

n(n-1) != (n(n-1)/n^2. n(n-1) definitely goes to infinity.

[guezz119]

damn. all this is coming back from the back of my brain when i learned this in high school.

[hytechmaiden]

ok, its complicated. =D

[chocolatecookie77]

thanx sweetie!

[NASSER5057]

WTF 0_o

[meow5887]

you might like to increase the volume of this video. great video.. thanx for posting...

[daedulus1]

how do u get teh -1?

[floydzia0210]

weeeeeeee

[5dArK5sOuL5]

HOLY FUCK MAN!

[ShadoWafel]

i guess ill come back in two or three years when i could understand it...

what lvl of math is it? (it is math right? it doesnt look like physiqs...)

[TheRaf87]

this is math..it wouldn't have sense if it was physics :D

[ziggy4mare]

leaving cert higher level maths im doing atm. heavy stuff.

[kramaster3]

1/3 * 0 = 0 right???? not 1/3 I don't want to get confused O.o

[Jesus0is0my0Savior]

@kramaster3 Yeah, it's 0.

[GetToDaChoppaNOW]

thanks

[appoolshark319]

isn't it convergent only if -1<R<1? (not < or = to 1)?

[BrianOJames]

no because it is a sequence and not a series (a summation)

[Jesus0is0my0Savior]

@appoolshark319 If it's 1 then any 1^n=1.. thus converging to 1.

[gladeplugins]

Your explanation for converging and diverging are BEAUTIFUL compared to what my Calculus book offers. Thank you, Patrick! ^_^

[Hashbrowniepie]

1/3 * 0 = 1/3 who knew lol.

[Alain0775]

Hey Patrick is there a way I can buy some video from you? Please let me know.

[marioxDD]

is that part at 10:50 the squeeze theorem ?

[hmoud]

thanx DuDe!!!!

[BajanCreation]

dude, are you a phd graduate, this is some serious maths, almost insane maths here. respond soon.

[Nanumir]

thanks for the video, I needed a remedial course in Calc II, III, and diffy Q, you are awesome.

at 10:36 is there any particular reason why the "generic number" has to be strictly less than -1

[Nanumir]

I meant strictly greater than -1

thanks

[inadaaaze]

the number inside the parenthesis (the number being raised to the n power) has to be greater than -1 (not less than as you said) or less than or equal to +1 in order for the sequence to converge. this is because any other number (for example, a number greater than +1, like 2) will result in a sequence that diverges. (ex, 2^n -> infinity)

[rryking]

10:53 how does 1/3 x 0= 1/3?

[patrickJMT]

clearly it is magic

[thelastmexican84]

Youre the greatest Señor JMT

[cafemaduro09]

I really appreciate this video it helped me a lot, thank you patrick JMT

[yegentube]

@youalldisgustme you are waste of Oxygen

[patrickJMT]

looooooooool

[OutrageousElephant]

haha only the best teachers say lol

[chadwickneutron]

1/3 * 0 = 1/3?!

[Arycke]

I noticed that also, struck me as a little...odd :)

[utheather]

magic... te he

[payasodundo17]

in the example that you give, dont you have to use L'Hospitals rule because its the limit of infinity times infinity?

[Luciana08E]

I was thinking the same thing, but then I saw my book. L'hopitals rule say that 0/0, inf/inf, -inf/inf, or inf/inf are indeterminate and can be extended to say that 0 x inf, 0^0, 1^inf, and inf^0 (also indeterminate).

However, it doesn't say anything about inf x inf, so it probably is equal to infinity and there is no need to use L'hopitals rule

[patrickJMT]

ya, it makes sense that it is not indeterminate... a big number multiplied by a big number is a big number... no ambiguity there

[youalldisgustme]

infinity is a concept, not a number, and as such there is no answer to infinity times infiniy. so it must be indeterminate then.

[MrTinyhippo]

youalldisgustme you don't understand what an indeterminate is! At least understand what you comment about!

[manoljo]

@Luciana08E that's incorrect. It's Bernoulli's Rule. L'Hopital was a marquis fraud.

[uarhara]

you don't know how many asses you helped by providing us this great help !! me and my friends always study from your videos we don't go to our classes anymore lol thank you very much man i hope you replay my message

[patrickJMT]

ha! go to class!!!!!!!!

[xylokid4]

hey

I was wondering about the interval of -1<#<+1. If the # raised to a power fits into that interval and is converging, it always equals to 0? Or was this just a special case? If so, why was it a special case?

[ZergFireX]

Cool video. :)

[14Anaid]

these videos are AMAZING! plus i LOVE the way you write!

[diomedes39]

Thank you Patrick! Your videos are so clear and if I am having trouble with a concept all I have to do is rewind. Thanks for your hard work

[supergsx]

How can, if the limit of A(sub)n in an infinite series as n approaches Infinity equals zero, can the series diverge?!?!?!?!?!?!

That question has made me lose sleep.

[patrickJMT]

well, you can show series 1/n diverges even though the terms approach zero... easy argument to prove it!

[supergsx]

Yeah that's what I was thinking...

But what value do you start with? Infinity?

[nmq3b]

Wow you're amazing Patrick! Very clear both verbally and on paper.

[patrickJMT]

thanks : )

[samurai165]

I get everything but how did you know it converges to zero though? Thanks for all the videos you post.

[SaMatta87]

Thanks to you I'm read for Friday's quiz

:^D

[feihtkrad]

We need more teachers/professors like you in our schools!

[patrickJMT]

thanks! i am about to go torture a group of students, and i do not think they feel the same!

[scientificboysclub]

WOW Awesome Vdo's !! Thank you tutor !!

[Mattprole]

Torture, aye? A freudian slip me thinks ;o