Using the Ratio Test to Determine if a Series Converges #2
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- Опубліковано 2 кві 2008
- Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Using the Ratio Test to Determine if a Series Converges #2 - Two more examples are shown using the Ratio Test. For more free math videos, visit PatrickJMT.com
hey, glad to help! i appreciate the kind comments; it is nice to know that my hours and hours and hours of making and posting math vids is helping make things a bit clearer for others out there!! take care, and good luck.
@daemonpacman ha, good luck! there is a sequence and series playlist with lots of stuff. you may also check out the videos on the right side (related videos) as some are missing from the playlist.
Hey Patrick! I just wanted to say that I was completely clueless on the factorial examples that my professor used to give, but when you said "think of it as 7! over 8!" etc, everything just cleared up.
Thank you so much man. I can't tell you how much I appreciate it.
You're saving my calc grade
I took cal 2 a year ago and these videos got me through it! I just recommended a baby freshman to this and i just had to go into nostalgia and watch this video again! Please dont take these tutorials offline! This is a relic of the internet.
whenever you get stuck on the 'generic notation' try to use some concrete examples!!! that usually helps to clarify things!
glad the vid helped
you've been saving my math grade since high school, and I am now a senior in college taking calc 2, thankfully this is my final math course, but truly, thank you for all the help!
glad it helps! i will keep posting!
@kakaboo nope; 1 ^ (infinity) is an indeterminate power; you can use l'hospital's rule to find its value. in this case, it is e.
I started watching your videos when I was still taking Calculus 1. You helped survive the semester! and now that I'm in calculus 2, I still come back to you, and------AAAH! THANK YOU!!!!
So. Much!
no problem!
you are very welcome!
yep
Thankyou! your videos are the most helpful, I use them to learn the material better and to review it for the test.
Probably the most helpful factorial limit video I've ever seen! Thank you so much!
Thanks for posting these videos about ratio tests, Patrick. But could you also please post a video doing step by step parts beginner level, right after you plug in the (nt1)'s and setting up the reciprocal? Literally, right after that is where I get so confused, when it comes to moving things around to clean up the problem before finishing. These just happen to be super hard for me, where it takes me a little longer to catch on and I have to see even the baby steps. In the end, I come out gunning out every problem when I can see how to do each part properly. Many thanks.
You are my life saver! All tutorials are easy to understand and very useful. Thanks!
@fuckinpete glad it helped!
Patrick could you please do a video playlist covering modular arithmetic please? It would be helpful to others needing help in that area.
Your explanation of cancelling factorials was so simple yet brilliant
Great explanation! You explained it better than my textbook.
OG youtube Legend!! I grew up with this guy teaching me math!
All I can say is: HOLY JESUS!
Man oh man you are a lifesaver. You are working out all the small trouble spots I have and now I completely understand it. Thank you so much.
HOW COULD SOO MUCH GOD GIVEN TALENT BE CONCENTRATED IN ONE PERSON?????im just hatin. Seriously you have a gift to break very difficult concepts down into easily understandable material.
that is great! good job!!
You are a great teacher, you make my college calculus classes so much easier. I wish you taught at our university, lol. Thanks again! :D
i love you. I have an exam tomorrow and was just about to give up on revision before someone told me about your page. Now I finally understand maths again. I'm not more confident going into this exam than I have been for any exam in the last 2 years. Thankyou. I'm telling all my friends forsure.
I wish I could have known you start of the semester, although my grade in Calc 2 is A but you making the subject much simpler than what I thought..... luv it ..... thanks....................
thank you! i was confusing with my assignment! have a nice day patrick!
why cant all math professors teach like you, your videos are beyond amazing
Thank you so much!! This is so helpful! I really appreciate it! :)
Thanks so much for posting this - you're very knowledgeable!
You are an excellent e-tutor. You are the sole reason I'm working on Calculus 2 at 13 years old.
happy i could help :)
umm wow
Love your work!! thanks to u i just finished a take home test!
Thanks alot sir I watch all of the vedioes related to ratio test.... WATCHING from Pakistan 🇵🇰
I haven't been to class in a few weeks because my professor is very hard to understand. I've been watching your videos instead...and i gotta say you are amazing. I wish you were my professor :) Thanks so much for posting these videos. Take care ^__^
Thank you Patrick!!!~your video help me finished my assignment!!!
finding you was the best thing that ever happened to me! Because of you, calculus has become more clear to me! Thank You so much! =D
I *really* wish I would have found these videos last semester (I would have felt confident enough to take Calculus II in the summer rather than this semester). But I am glad I found them when I did, and you can believe that I will be spreading word about these videos. Great job.
HL math option: Further Calculus, thanks patrick! Saving my life right here!
well, the limit would approach 0, so you would have 2* 0 = 0
Thanks alot dude, you've really helped me❤💪💪❤
thanks friend : )
glad you like them!
thanks so much i hope you realize how much help you've been!
thanks mate, this really helps alot.
Patrick. Thank you so much.
@tmac1ninja i wonder if the chinese would put everyone under house arrest and not let me go
you help me a lot thank you soo much!!
yes, and i already have a few
glad i could help :)
You are man PATRICK.Thank you.
u are a REALLY good teacher thanks alot :D
patrick you have saved my life , thank you so much
I got convergent for the first example you did.
I simplified it initially to get n/(3*27^n). Then using the ratio test I get |(n+1)/n * 1/27|. Then when you take the limit you get 1 * 1/27. Which would be convergent... What did I do wrong?
Thanks a lot for helping
Thank you. Why didn't you compute (-1)^(n+1) in the last problem?
this helps!!!
and i'm in grad school!
thank you and god bless for the videos! seriously!
WOW u are awesome...I LOVE U!!!...u make math look easy...which gives me hope..thanks again :)
THANK YOU SOOO MUCH MAN ... I REALLY APPRECIATE WHAT YOUR DOING ... THANKS AGAIN :D
@kingstun ha well, it did not just magically happen. i worked my ASS OFF in school.
You are a life saver!
Thanks a lot!
Thanks a lot!!1 You're brilliant!
you are amazing!!!! a=thank you!!1 i was wondering if you had any videos on why the ratio test works? like a proof? also the same for other tests eg integral test?
Kind Regards Vegan Patel
Hi, Your videos help me so much. The only thing i have trouble with is knowing what test to do for each question. Do you have any tips for me?
lectuers r rubbish at describing this stuff but ur vidoes helped me alot =]
cheers man
ur videos r awweesome
u r a legend
Wow, you're the Paul Hewitt of Math! Thanks for the video!
@6:07 of the video when you expand the terms, how are you grouping them? In your earlier video they seemed to keep the same order but as the problems get more complicated the order of terms seem to switch. Are you just looking at which numerators and denominators have like exponents and using that?
someday, I'd totally include you to the list of people that helped me graduate college! thanks
It was actually helpful
Why is there modulus ?i am a bit confuse... i was informed that you have to use modulus when you are answering interval of convergence type of question hmm help me out anyone ..btw thanks for the video once again your vid help me alot for my calculus 2
no problem : )
and.... go to class : )
You always tell us "secrets" I feel like my proff does't tell. Should get an A with your help!
Hello, how do you decide which test to use?For example i am given an array/series and i need to conclude whether its converging or not. How do I start and how do I know which test to choose first?
How do you know when to use this ratio test?
my teacher knows nothing about explaining comparing to you... omg i love this! T_T
@mattazio
When we do the ratio, we're no longer working with the same function. The properties of our ratio is different from the original series and therefor different conclusions need to be made. You're right that the ratio would be divergent, proven by p-series. However, we aren't looking to see if the ratio is convergent or divergent, but whether it tends towards a number less than, greater than, or equal to 1 as it goes to infinity. This tells you if it converges or not.
when i get a degree and start making money, i will donate to patrickjmt before i make a donation to my school. so helpful, thank you
this is awesome.
@mattazio
A good analogy would be a function and it's derivative. If we're looking for a min/max on f(x), we would be looking at the zeros of f'(x). We will likely find that the zero of the derivative is not a min/max on the original function, because we performed an operation (differentiation) which fundamentally changed our function and it's properties. This is similar to the series-ratio relationship because we performed an operation (division) on the series which fundamentally changes it.
@oexnorth remember 2^2 = 4 . This allows simplification down to:
lim[ 2^(2-n) / 2^(2-n-1)]
Thank you!
Is it because of l'Hopital's rule that you can conclude that the limit becomes zero when the power in the denominator is higher than the highest power in the numerator? And that it becomes one if both have the same highest power (as seen in video part 1)? Thanks in advance for your help!
you are my hero :)
Thank you
i have my calc 3 midterm in 2.5 hours and this helped alot lol
im getting an A because of these vids. thanks man!
Can you explain how you got an "e" out of (1+(1/n))^n?
What if there is 1/(2n)! ? How do you cancel out and set up that problem to determine it is convergent?
@patrickJMT do you mean that limit->infinity [(n+1)/n]^n = 1^(infinity) = e?
or do I just apply L'hopital rule directly to limit->infinity [(n+1)/n]^n? even so, I dont see or get where the e would come from....
1 question
How come you didn't expand the (n+1)^2/n^2 ?
+Mazin Elobeid =[(n+1/n)]^2
@mattazio
"We will likely find that the zero of the derivative is not a min/max on the original function"
this is meant to be "not a min/max on the derivative"
thanks bro
but if lets say the limit equaled 1, we would have to use a different method.. possibly the alternative series test to find its convergence?
What would you do for 1/(4+2^(-n))?
You used this example in one of your root test examples and I personally think the root test is easier for this problem :)
how about if the highest power of the numerator is greater than the highest power of the denominator? is it closer to infinity
Sorry for being so dumb, but is the series convergent on 0, or whatever number you get? Or is the test only conclusive that the series is convergent/divergent?
Hi patrick, love your work and all but i tried this method on the sum of (2^n)/n! (basically same problem) and i got the answer 2*(lim n->infinity of 1/(n+1)) which is = 2 which should tell me that the series is divergent. The answer is Convergent though and i dont understand why :/
Umm just a question, at 7:45, shouldn't the (n+1) on the bottom cancel out with one of the (n+1)'s on the top? You've got (n+1)(n+1)/(n+1)n^2, since (n+1)^2 is the same as (n+1)(n+1). So, you should get (n+1)/n^2... then evaluate the limit.
thats what I thought, did you ever figure out why he didnt?