The Binomial Series - Example 1

[masterblake9]

Exam tomorrow. I'd be lost without this!

[patrickJMT]

@masterblake9 good luck!

[vinvinnabulation]

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.

[dickenzon]

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

[thefearlessunicorn]

awesome!!!!!! clear and simple!!!! keep up the good work man and thanks for dedicating your time into this!!!!!

[patrickJMT]

@thefearlessunicorn you are very welcome

[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

[MaksimBFF]

where is x^n at the end of the sigma notation?

[waseeawas]

you are amazing! I watched your videos day before my first year calculus exam and no lie I aced it!! now I'm taking 2nd year stats and I'm back searching for your videos all over youtube:) thankss sooo muchhh !!

[runback1983]

did you forget the x^n part?

[aopdjasldksa]

You should buy a white board haha. You'll save on paper costs, or you can use a mirror if you have a some lying around. That's what I use for scratch work when studying/self made calendars. :D

[its2in0the1numbers1]

WOW, my math teachers suck!

[ncvc14]

you forgot the (-1)^n in your end series.

[princesavolante]

Patrick you should look at the camaraaaaa

[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?

[JaktheAtheist]

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

[pstlwhppd]

patrickJMT has the coolest sigmas ever.

[calimikester]

I believe kCn = k!/n!(n-k)! only when k is a positive integer. It doesn't hold for real numbers.

[cantbelieveitsBUDR]

wait nvm. disregard my last comment. i interpreted it incorrectly.

[cantbelieveitsBUDR]

at 5:15 if n=0, isn't n^(-1/5) going to be undefined?

[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

[patrickJMT]

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

[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

[patrickJMT]

@honeypot11 ha, i hope it went well! A++++++

[Ch4nster]

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

[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!!!

[alexhamster1134]

0:11, the sigh of boredom :D

[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!

[wakpy]

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

[hdrevolution123]

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

[janitarjanitar]

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

[scdlbrdr]

Isn't the final answer supposed to be alternating. A (-1) ^ n went missing somewhere. Unless I missed something. And you forget an x^n in the final answer.

[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

[rohit91]

<3 pjmt <3

[wavy312]

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

[Rachman01]

you make my Calc 2 teacher look like a farting orangutan..

[masterblah777]

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

[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

[kofi246]

ur a God sens

[gerewinedladera3]

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

[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

[lIPerfectIl]

Notice at 3:05 how there is a 1/2 in front of the series. At 6:43, he distributes the 1/2 to every term. That means that the powers of 2 in the denominators will all go up by a power of 1.

[JakabBigShow]

oo ok, thanks for pointing that out for me

[speedboarding100]

i believe there is another formula for binomial series:

(k(k-1)(k-n+1)x^n)/n!

[Brianaust138]

where the 1/2, that on the second line of the solution came from? How did u calculate it???

[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.

[fred2028]

These videos will be the only reason I will hopefully pass Calculus 2.

[seamus4now]

Dude, I think i can just burn my textbook with confidence with your infinite series of videos (no pun intended) They are great!!

[beanboy5555]

thank you, ur vids are a big help for studying

[MRIYBR]

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

[anat1992]

perfect review for the ap test

[Katianie9]

These videos are absolutely amazing. I'm I'm college taking calc2 right now and I don't think I would have the understanding I do if it weren't for these videos. Thank you so much

[patrickJMT]

happy to help!

[SirHadouken]

mines friday can you take mine too?

[philboy521]

can you take my test this thurs for me

[patrickJMT]

sure, why not

[jagua1234]

Thank you so much

[dipsetmeng]

when writing the power series at 3:20,

shouldn't it be (x/32)^n instead (-x/32)^n

[rathwej]

i think youre right

[007oscar]

Dude! your videos are great!! thanks so much, I've pretty much learned everything i know about series from your videos and I'm a first year engineering student!

[runnerman89]

So have you ever considered coming to Purdue to teach?

[loveart01]

shouldn't you have an x^n at the very end of the answer?

[shim2dawg]

great!

[bignickkk]

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

[hobin02]

nice video....

[AnonNov]

Man that's one heavy *sigh* you let out before you started stating the binomial series ;D

[kentorwow]

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

[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.

[jagua1234]

I am in highschool and I have a test over this.

[alancaster00]

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

[javalu882005]

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

[yuotubepuntocom]

yeah, I noticed that after I did the coment. Thank you anyway, and I am sorry, it was my mistake!!!

Have a great day!!

[javalu882005]

hehe, any one could make that mistake =)

[diwr]

nice demo!

[sushiplaza]

Thank you for the post. I just took my midterm about this and series tests yesterday.

[Nandine2]

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