❖ The Binomial Series ❖

[@kimtran9336]

Thank you for the video 13 years later! The pandemic has made university completely online and it's been extremely difficult to learn calc 2, but your videos are a lifesaver! Thank you!

[@masterblah777]

You are one of the best math instructors I have ever seen...better than any of the calc teachers I've had...

[@sonichedgehog36]

I figured out after having going through your videos that you must get a lot of money from the ads played. So many people using this, so many ads being played, all besides the donations you receive, must have made you rich by now. Thank you for the help!

[@yesiwouldlikecake]

Thank you sooo much! My final's bonus question was a binomial series question and I got full credit because of your videos! Helped me get my A in Calc II.

[@nikitaboris1124]

God bless you without your videos i wouldn’t graduate

[@ShadyMan01]

Everything in the denominator is raised to the 1/5th power, the same as saying the 5th root. The 5th root of 32 is 2, he has just split the numerator up so it now reads as 1/2 X 1/(the rest of it) to get it into the form of the power series shown at the start.

[@terwizzyvee]

You must be in my will, PatrickJMT. Nobody makes me enjoy math like you do!

[@janitarjanitar]

i just donated through the jmt site because of your whole power series section. I LOVE IT!! ill be honored if you put the money towards some more super leaky paper

[@romal6793]

13 year old video helping for my exam 🔥.thanks man

[@Carichic15]

I wish you could teach at my school. Im talking this foundations of advanced math class and my professor doesn't know how to teach and expects us to know how to do all of this. You are great!!! Thanks so much!

[@lorrainekateramos]

this really help me a lot. I need a hundred of examples of application of power series in statistics. Thanks for making this.

[@patrickjmt]

@thefearlessunicorn you are very welcome

[@05brk67071]

You do such a great job with these videos, and you make it look so simple. Just one question on this video: Did you forget about the x^n or did it disappear legally?

[@jordanagnew7071]

Yes the videos from 2006 (or 2008) are really helping.

[@awininegeno]

i tore a muscle a missed a good week of school. My math teacher offered that i can take my test next week, but im manning up and taking it tommorow!

[@tiisetsomashele7077]

I'm confused AF

[@akilakavisinghe7189]

LOL how? It's really not that difficult you just have to listen closely. Literally just rewriting something and plugging in numbers into a formula.

[@akilakavisinghe7189]

Also realized this was written 2 years ago... hopefully you understand them now.

[@koketsokotsane9936]

Legend has it the Test came down on him like Satan himself and he never showed his face in public again.

[@thomasgalarneau2928]

It's not that the arithmetic is difficult, but truly understanding what's happening is the challenge, for me atleast.

[@masterblake9]

Exam tomorrow. I'd be lost without this!

[@Engineer1T6]

A nice way to rewrite the binomial series terms generally (for every term after the first, since term 1 is always 1) you can say that sigma (p choose k) x^k = sigma [p(p-1)(p-2)(p-3)...(p-k+1)/k!)] * x^k that gives you each term, just plug in your p and k

[@hdrevolution123]

Holy frick! You make a seemingly difficult topic look so easy! Your videos are so accessible! You are definitely getting my subscription!

[@gartyqam]

ok

[@Cramerica66]

Don't quote me with this, but I think the theorem is the algebra rule of (K over N) while in series we use (K over N) multiplied by X^N as we approach infinity. From my understanding techniques like this is what is used for programming in electronics like calculators. But like I said, don't quote me since I am just a simple college student. ;)

[@sfundomabaso3200]

when you expanding your series(at the 7th min), isn't the 3rd term supposed to be negative since you're multiplying by 3 negatives? (-1/5)(-6/5)(-x^3/(2^15)

[@MrTeamFoolish]

Only part I do not understand is the denominator section of 2^(5n+1). At the beginning, we simplify our (-x/32)^n to ((-x^n)/(2^(5n)). Where do the extra set of 2's come into play? Especially when n=1, as you only have (-1/5)(-x/2^5).

[@evelinventura7402]

For the final answer don't you need to include the x? Like x^n?

[@manchesterrockinable]

Yes, You do need to include x^n. I guess he forgot about it.

[@111dallas1111]

Thanks Patrick for making math easier xD

[@ken8844]

you forgot the x^n

[@patrickjmt]

happy to help!

[@dickenzon]

this may be a stupid question but what is the difference between a taylor series and a binomial series?

[@GuildmistressDeby]

in the numerator...why is it (5n-4)? i know where you got the 5n from, but i don't know where the 4 is coming from. thanks. btw, LOVE UR VIDS!!!

[@Scofields1828]

Can anyone explain the algebra at the end? At the timeframe 7:00, I don't know how he got 1/(5*2^6) etc

[@TheUltimateGeminiHasSurvived]

Everything is multiplied by the 1/2 we factored out in the beginning.

[@kentorwow]

can you start the series with 0 and put the 1/2 in? then the 5n-4 thing would be weird

[@Engineer1T6]

thanks! got a Calc B exam tomorrow, this really helped.

[@mamu7mich]

what's the difference between binomial theoram and binomial series? are they both the same thing?

[@JakabBigShow]

why does the powers of 2 go from 10 and 15 to 11 and 16, im not seeing that step, if u could let me know that would be great! Thanks

[@animeniack]

Thank you so much for these videos Patrick, you're amazing! Correct me if I'm wrong...But shouldn't the answer have x^n at the end too?

[@reimasashi]

You left me hanging with your explanation, I'm not good at math thats why I'm watching, but with that explanation, it makes more confuse

[@JabooK]

Uuuuu yes, sweet knowledge. Exam next week. Patrick this week. Don't we love it!

[@AyJay2303]

have you guys noticed that everyone looks up patrick a day before the test or mb a few hrs before the test....lolz

[@abed.al-sqoor4598]

I guess that you forgot to write x^n with the final series. Thanks a lot for your videos.

[@MRIYBR]

have you done fourier series somewhere? I'd really love to learn it from YOU.

[@tytypar]

Where do the x terms go in the final sigma notation?

[@syedmdabid7191]

What-th term is 3y z^2 in the expansion of (x+y+z) ^3 ? (3 second)

[@RPMOORE16]

dude how many sharpies do you go through?

[@w-a-v-y]

You forgot the x^n term in the series you wrote down the end

[@lonewolfnh89]

Don't know why I'm typing this but I guess it has something to do with the 2 Rockstars I had through the night. I'm about to go hard on this exam baby. I'm doing it for you patrick i'm going in there guns blazing. When I'm done i'm gonna flip my exam over and write "In Patrick we Trust." I love you man.

[@shellea3]

HI love the videos, very helpful. I have a question for you. How would I use the binomial theorem to expand 1+2x to 4 terms and use this expansion to find an approximate value of 1.2. Thanks so much

[@zbro460]

Exam in four hours, so thankful for these videos! My professor just can't explain things very well...

[@gartyqam]

what u doing here

[@danielremus1811]

What happened to the x^n at the end of the video?

[@Naked_Snake]

Never heard you use the word "basically" so many times in a single video. :)

[@lawrencesibusiso741]

how do you solve problems with the final sum ending at the "nth' term, were n is not defined?

[@gerewinedladera3]

our teacher had an another formula for binomial series... now im confused which one i will use..

[@metabog]

Are american kids learning this in high-school? We did everything about this stuff as well as harder Group theory and integrals and stuff, and when I moved to england for University I noticed those people haven't even studied logarithms.

[@patrickjmt]

sure, why not

[@pstlwhppd]

patrickJMT has the coolest sigmas ever.

[@sfundomabaso3200]

Why is it that you left out, or ignored the negatives

[@DescartesRenegade]

did you forget the x^n part?

[@neerajtiwari5365]

Can anyone explain to me why we required |x|

[@masterblake9]

I don't understand. I used this video for learning, and later reviewing the subject. What do you mean "waited so long before learning"? You are aware that you can watch videos multiple times at different times, right? Also, engineering? I'm not becoming an engineer and my grades are quite good...

[@alancaster00]

there is a mistake because instead of raising to to the 1/5 it should be 2/5 because of the square root

[@harrisonholt8015]

Went to your website, and I've always wondered what you looked like because all I see is your hand haha.... you were exactly how I thought you'd look. LOL

[@wakpy]

Hey dude, thx alot man... i'm now able to do my assignments confidently. :)

[@guitarndbattlefield]

What if it's non-Maclaurin? I'm having an issue trying to figure these out as binomial series that are centered about anything but a = 0.

[@sanchitsingh7162]

Same dude

[@nunyabeezwaxx4586]

You forgot x^n in your final answer

[@PrisonbreakCB]

If i try to find my n=0 term using the binomial series i dont get 1 as the first term why is that? :S

[@danielavrit4526]

PatrickJMT is the P90x of math

[@janitarjanitar]

my new favorite phrase in the english language: "Alright, in this video..."

[@aldotb]

Hey... Patrick you are the ONE... I think that much better that some MIT Phd teacher ... I will follow you and thank for make that people like me to learn from your knowledge thank you.. Aldo

[@AhmedRaza-lr7uw]

+Aldo Tamariz You have to remember that professors do teaching as a side job. Their careers are research, not teaching. :)

[@sekmanimohamedamine1237]

very difficult and you choose a difficult exemple

[@roudhaaraimy4815]

From where you got the 1/2 ????????

[@kool45520]

Originally, the equation was 1/(32-x)^(1/5). The form needs to be (1-(expression))^(Kvalue). So what he did was factor out the 32, and took the fifth root of that, which is 2. Now the expression is 1/2[(1-(x/32))^(-1/5)]

[@mollyc2575]

What's the value of -1/5! Does it exist?

[@Nandine2]

thank you so muck, I love your videos, they are very intuitive

[@philliyphil]

amazing vid man! helps out a lot and i got a midterm 2mo!

[@patrickjmt]

@honeypot11 ha! now just hear my voice during your exam...

[@hks8997]

for the fist time i watched your vid and im still confused :(

[@xUdieToox]

I have not taken a mathematics course in 2 years. Sometimes I feel it is too late for me to get back into shape :(

[@ivangushkov3651]

When you think like this just remember that some of us were never ''in shape'' :P

[@udecide0010]

did know one else notice that the negatives just disappeared when he multiplied 1/2 in

[@shalomgomez8063]

You had 1/2[1+(-1/5)(-x/2^6)+(-1/5)(-6/5)/2!*(x^2/2^10)....and then rewrite it as 1/2[1+(-1/5)(-x/2^6)+(6/5^2)/2!*(x^2/2^11) ... why is it 2^11 rather than 2^10?

[@cjordan921]

reviewing for a calc 3 test on june 7th.

[@JaktheAtheist]

Thanks for the videos patrick, but I wish you would have done a really simple example first.

[@futuregamer6866]

4:48 Ohhhh I felt that

[@Leonitusworm]

Screw that class. I enjoyed the use of what it gave me after I took it but that was a difficult class my friend. Good luck on that test.

[@anantsaxena8605]

a doubt... how is (-1/5)Cn even possible?

[@Ch4nster]

If I had a million dollars and I gave u a nickel for every view, I'd be in the negatives

[@brittanydean638]

hey i don't understand how u got 1/2????

[@jarrhead20]

(32)^(1/5)=2

[@brittanydean638]

ok thank you i figured it out after i walked away from it for awhile!!!!!

[@pascal3934]

+jarrhead20 thank you but so why he put 1/2 instead of 2; thanks for your answer

[@pascal3934]

+jarrhead20 forget my question

[@dood9971]

Haha... It's summer and I'm watching this

[@limitsatinfinity4393]

Thank you patrick

[@philboy521]

can you take my test this thurs for me

[@diwr]

nice demo!

[@edisondotme]

Patrick, watch your overusage of the word "basically." Thanks for the video.

[@javalu882005]

no, is a 5 th Root not a square root.

[@taylorandrosen]

isn't it just (5n+4)! on the top?

[@bigDeeOT]

No.

[@SirHadouken]

mines friday can you take mine too?

[@SehamArad]

did you forget the 'x^n' in the final answer??'

[@SehamArad]

why did we ignore the fact there are negative in the 07:16 section.

[@INDesign818]

good method ... and send video of sum of square of N number

[@princesavolante]

Patrick you should look at the camaraaaaa

[@honeypot11]

hehe im using my "special headphones" while listening to your videos and your voice has this echoe-y godly feel to it xDD /random

[@honeypot11]

@patrickJMT looooool! yes, through the power of telapathy, i was able to hear your very echo-ey voice and imagine the sheets of paper with the equations on them xD anyway, wasn't too bad, if a little intense with soo many students in one room and T.A's walking like guards up and down the aisles =P aaaand surprisingly no binomial series on it -thumbs up- :B

[@JakabBigShow]

oo ok, thanks for pointing that out for me

[@derekjohnson3550]

the fifth root of 32 is 2, so he just factored it out

[@patrickjmt]

@masterblake9 good luck!