The Binomial Series - Example 1

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Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Using the Binomial Series to derive power series representations for another function. One example is shown!
For more free math videos, check out PatrickJMT.com
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11 сен 2024

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Комментарии : 141

@kimtran9336 3 года назад

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 14 лет назад

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

@tiisetsomashele7077 8 лет назад

I'm confused AF

@akilakavisinghe7189 6 лет назад

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 6 лет назад

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

@koketsokotsane9936 6 лет назад

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

@thomasgalarneau2928 5 лет назад

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

@yesiwouldlikecake 12 лет назад

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.

@sonichedgehog36 11 лет назад

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!

@romal6793 2 года назад

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

@terwizzyvee 6 лет назад

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

@Carichic15 14 лет назад

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 12 лет назад

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

@masterblake9 12 лет назад

Exam tomorrow. I'd be lost without this!

@ShadyMan01 15 лет назад

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.

@Cramerica66 11 лет назад

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. ;)

@janitarjanitar 14 лет назад

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

@ken8844 10 лет назад

you forgot the x^n

@Engineer1T6 11 лет назад

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

@111dallas1111 9 лет назад

Thanks Patrick for making math easier xD

@sfundomabaso3200 7 лет назад

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)

@nikitaboris1124 4 года назад

God bless you without your videos i wouldn’t graduate

@patrickjmt 13 лет назад

@thefearlessunicorn you are very welcome

@hdrevolution123 14 лет назад

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

@gartyqam 3 года назад

@patrickjmt 15 лет назад

happy to help!

@awininegeno 11 лет назад

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!

@MrTeamFoolish 7 лет назад

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).

@DamnYouDamnMe 10 лет назад

Great video, thank you. If I may ask though isn't the convention to take the binomial coefficient as 0 when the bottom is greater than the top or this is just something we do in Statistics?

@harrisonholt8015 12 лет назад

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

@Engineer1T6 11 лет назад

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

@evelinventura7402 10 лет назад

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

@manchesterrockinable 10 лет назад

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

@05brk67071 12 лет назад

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?

@JabooK 11 лет назад

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

@pstlwhppd 13 лет назад

patrickJMT has the coolest sigmas ever.

@lonewolfnh89 11 лет назад

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.

@jordanagnew7071 5 лет назад

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

@abed.al-sqoor4598 8 лет назад

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

@AyJay2303 12 лет назад

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

@reimasashi 7 лет назад

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

@hks8997 6 лет назад

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

@Nandine2 16 лет назад

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

@dickenzon 12 лет назад

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

@JakabBigShow 15 лет назад

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

@philliyphil 15 лет назад

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

@wakpy 14 лет назад

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

@patrickjmt 15 лет назад

sure, why not

@kentorwow 15 лет назад

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

@danielavrit4526 11 лет назад

PatrickJMT is the P90x of math

@animeniack 13 лет назад

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?

@metabog 15 лет назад

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.

@Naked_Snake 12 лет назад

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

@zbro460 12 лет назад

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

@gartyqam 3 года назад

what u doing here

@RPMOORE16 11 лет назад

dude how many sharpies do you go through?

@mamu7mich 11 лет назад

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

@GuildmistressDeby 14 лет назад

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!!!

@sekmanimohamedamine1237 5 лет назад

very difficult and you choose a difficult exemple

@patrickjmt 13 лет назад

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

@w-a-v-y 14 лет назад

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

@nunyabeezwaxx4586 6 лет назад

You forgot x^n in your final answer

@tytypar 12 лет назад

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

@masterblake9 11 лет назад

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 16 лет назад

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

@Leonitusworm 11 лет назад

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.

@shalomgomez8063 9 лет назад

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?

@danielremus1811 11 лет назад

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

@Ch4nster 14 лет назад

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

@sfundomabaso3200 7 лет назад

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

@limitsatinfinity4393 8 лет назад

Thank you patrick

@lawrencesibusiso741 11 лет назад

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

@MRIYBR 15 лет назад

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

@PrisonbreakCB 14 лет назад

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

@syedmdabid7191 4 года назад

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

@shellea3 13 лет назад

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

@honeypot11 13 лет назад

@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

@aldotb 10 лет назад

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 9 лет назад

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

@diwr 16 лет назад

nice demo!

@JaktheAtheist 13 лет назад

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

@DescartesRenegade 13 лет назад

did you forget the x^n part?

@gerewinedladera3 14 лет назад

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

@honeypot11 13 лет назад

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

@neerajtiwari5365 7 лет назад

Can anyone explain to me why we required |x|

@edisondotme 11 лет назад

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

@janitarjanitar 14 лет назад

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

@roudhaaraimy4815 9 лет назад

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

@kool45520 7 лет назад

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)]