Geometric Series and the Test for Divergence - Part 2

[bmazymei]

Even though I got a 37 on my exam before my final because my professor is a pompous prick with a 50% pass rate, watching your videos helped me ace the final and pull out with an A in my calc 1 class, thanks so much!

[linocutter]

ugh.. why didn't I watch these videos earlier in the semester.. !!

If I did, I would not be stressing so much about the final and I would definitely end up with an A in my Calc II class

[Gazzawey]

@linocutter same here my final is tomorow and this series driving me crazy

[Billabong024]

freakin awesome dude. I just learned this thing today and you make it so much easier.

Also I got a 100 on my 2nd test on integration!

Thank you

[patrickJMT]

@Billabong024 good job!

[mangaliewa]

how can you dislike a fucking good educational video? wtf

[fairykat1]

so finally this series converges na??

[djsneaks2]

nvm your right don't lesson to that post i posted.

[djsneaks2]

i think you fucked up on this part, dont you have to change you index to be [whatever] ^ n-1

insted of just n? to match the geometric seriers of starting at 1? ar^n-1?

now if you started at ZERO you would want [whatever] ^n

but in this case it starts at 1, so i think this problem is wrong.

if im wrong its whatever.

[suny123boy1]

You helped me pass my Calc II class, you're the man. Why can't all teacher be as good as you? Are you a professor? You should be.

[FrigginSmift]

I learn more in one of your 5min vids than i do in my 2hr lectures

[danthemanpatrick]

help, thy name is patrickJMT

[NeoMadison]

Thanks so much for the vid. I was feeling really dumb, not understanding the text book but this helped a ton! Would you also have an example of finding the convergence of geometric series with alternating signs? Thanks a ton for your time and clarity, you've done much to subvert the idea that math is hard and only for a select 'smart' few!

[ritual78]

Thanks Patrick, your videos are great help for me to understand calculus.

[mamatela]

you're wrong...... ((1/3)/1-(2/3))= 3/2

[pointed8]

@mamatela As you can see yourself, everybody makes mistakes !

[The1ntern]

I like how the advertisements before the videos are for Educator.com

[patrickJMT]

@The1ntern well, math videos seem like a good place to advertise math videos : )

[jhh1822]

love your videos (as does everyone in calculus at Brooklyn College)

I think there's a very small computational error at the end of Geometric Series and the Test for Divergence (part two) -- you say that the second series converges to 2 but I believe it converges to 1/2 (with the sum of the two series converging to 3/2).

[patrickJMT]

@jhh1822 ops yes, my mistake!

[tpubill]

you are a much better teacher than my current calc II teacher. you make series seem so easy. so thank you so much. you're a life saver :D

[gjmottet]

Great video, your uploads are a god send. From my understanding of my textbook r must be between -1 and 1 and not equal to zero otherwise the geometric series diverges. I tried it and it seems to work. Just wanted to point it out.

[The3jji]

The series converges to 1.5

Please check if its correct :)

[DonChedda]

@The3jji Correct (1/3)(3/2) = 1/2 not 2 =)

[patrickJMT]

@DonChedda opppps! i am just making sure you all are paying attention

[xXBigTacoXx]

can you make a proof for the divergence test??

[like9orphanz]

I tutor math at the school that I go to and I'm in cal 2 right now, whenever a student and I cant figure out a problem I always tell them to look up your video and everyone always figures it out :)

[patrickJMT]

@like9orphanz perfect : )

[ogre61691]

thank you.

[koerbemd]

Patrick, I don't know if someone has mentioned this, but is (1/3)/(2/3)= .5, and it would diverge to 1.5... Unless I made a stupid mistake somewhere, which is 100% possible. Thank you so much for the videos though. I use your videos more than my lecture. Calc 2 midterm t-minus 16 hours.

[iltns22]

@koerbemd you are right, that is his mistake so it should coverge to 1.5 or 3/2 same thing.

[Tweak2727]

I know multiple students from UNLV would like to thank you for all the videos. The videos help solidify what we are trying to learn from the classroom! Keep it up!

[patrickJMT]

@Tweak2727 a big 'your welcome' to all the unlv students!

[mosum91]

this is fantastic and so easy to follow, plus you have good handwriting :) thanks!!!

[patrickJMT]

@mosum91 you are welcome

[DashofDosh]

thank you patrick! I treat calculus class as a free period but learn at night when I watch your videos.

[patrickJMT]

@DashofDosh ha - now i feel pressured to make good videos!

[acrsurfing]

Thanks, if i pass my midterm, you deserve the credit cause my calc teacher sucks

[fizzmaverick]

great vid!!! hepled me alot!

[saas2244]

GOD BLESS YOU .

YOU ARE FANTASTIC 

[dillmon1]

YES!! I actually understand this shit now!

[dfts22e]

Please make more sequences and SERIES videos!

[noeldier]

Quick question - I thought the rule for geometric series was that it would be in the form: (a)(r)^n-1 but in this example they are just (a)(r)^n with a being 1. Can you please clarify this for me - cheers for all the videos.

[knightsfever]

yo are amazing and so helpful i would have loved to have you as a prof

[aboveall0006]

1/3 divided by 2/3 = 1/3 x 3/2 = 3/6 = 1=2....therefore it converges to 3/2. Just a little confusion on that last part, no biggie, keep up the great teaching Pat!! Thanks for keeping my grades up!

[unboundos]

your awesome man thanks for all the videos

[eviltwin1000]

You are a fantastic teacher! Many professors are doctors, etc, but they're not meant to teach! You make things a lot simpler and make math fun!

[lifematch]

patrick i have been watching ur videos from limits to here. I pretty much learned calculus from your video rather then the text book and prof. Don't like to admitted but i skip my math class all the time cuz your video are much better then my prof's lecture. Your video has been a huge asset in my life! i would like to take this chance to wholeheartedly thank you for everything you have done for us. Please keep what your doing best and hope all your life problems will be solved (if any)!

[sjprep7]

Hey just wanted to let you know that your videos are really helping prepare for my Rutgers Calc II final. Thank you so much for giving your time to help me out.

[guitarsniper1]

im left handed.....im not smart im just in 2nd year high school and stuck with a teacher that teaches collage stuff and calculus w/c brought me here

[Ledarifique]

Why are the cool and intelligent people always the ones to be left handed?

[ChuiaPoil]

Hey patrick I think you forgot to add this video to your "Sequence and Series Video Tutorial" playlist.

Thanks for the videos. :)

[skatz2live]

Dude keep doing what your doing, ive been studying for a calc 2 final all day, and ive been watching a bunch of your videos, they are soo much help. No joke your way better than my professor.

[rwiebster]

sometimes i think they should start a youtube university.

[BPColin]

I learn more here than i do in class... sounds like a plan to me. university for the next generation...

[ch3ssco]

i didnt go to a math lecture all semester, and i just penetrated a past exam paper thanks to a couple days of textbook/internet. looking foreward to my exam tommorow :)

[kiaracm]

A geometric series converges if -1<r<1. So

(summation) ar^k= a/ 1-r

here a is 1 for both sums, r is 1/2 and 1/3

so why is the numerator 1/2 and 1/3?

[bryanj12341]

cool videos!

[jimmy3tymes]

is (1/4^n) = (1/4)^n?

[Cloudtheclow]

yes, since the but only because the top number is 1. If it were anything else this wouldn't be true. It only works with 1 because no mater what you raise it to the power of (n for example), it will always be 1.

[andreablacker]

only because 1 elevated to anything gives you 1... if not you couldn't do that.

[bryanj12341]

yup

[lyoung1988]

Sorry dude it converges to 1 + 1/2 = 3/2 ..anyways nice wrk!!!

[naylin369]

you forgot to flip the fraction when you divide. I think u got it wrong the answer is thus 3 not 3/2 please check again.

[MrPopenator]

3/2 is the correct answer

[jtnorg]

wait....(1/3)/(2/3)=(1/2) correct. so doesnt it converge to (3/2)

[ngwhizkid4christ]

Nah, comparing the series, when one converges, both converges. Note that the abs r is btw -1 and 1

[mnstrgdflla]

how does that answer the question?

[cyrax412]

This is the best help i've ever gotten, its so clear. Keep up the videos my professor doesnt speak english so i dont learn well.

[chopperwtfreed]

first view, cool