Root Test for Series
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- Опубліковано 25 тра 2008
- Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Root Test for Series - Using the Root Test to Determine if a Series Converges or Diverges! The test along with 3 full examples are shown!
For more free math videos, check out PatrickJMT.com
Still depressed that I've learned more from an hour of your videos than a month of class.....
well for one thing, He doesn't go over proofs, which are extremely abstracted. He just tells you how to do the concrete part of math: solving. The simplicity of the way he teaches plus the fact that the videos are short and convinient makes it easy to learn here. The people coming here are also in the mindset of learning too, otherwise it would be unlikely that they'd come here at all!
Almost 13 years later.... still amazing. Thank you so much for this. It's taught timelessly.
yes
Damn man i was 3 years old when he uploaded this video, and now look at me watching this video after all these years! UA-cam is great
glad you like them all : )
i figured that if they suck, i would just delete them. most people seem to like them though : )
and honestly, i forget half of this stuff, so i make them for 'future me' - the one that has forgotten and re-watches old me (newer me?), so i have to be nice and soothing to my future self : )
6:11 "The numerator is going to get big very quickly, the numerator is going to get big as well, but not as fast as the numerator." Idk why I found that so funny, probably too much studying...
Dude, I was literally tweaking out about this midterm that I have to take in like 40 minutes and your videos on convergence tests totally saved my ass. Thank you, Patrick.
"Tired of scrounging youtube for math help?"
No, I've found this channel. Why would anyone pay for online tutoring videos if they've found patrickJMT?
7 years down the line and us bloaks still get that stupid ad lol
well, it is basically knowing that the n/(n+1) is the flip of (n+1)/n; that raised to a power of n has something to do with 'e'! i am seen that limit so many times now, that i just recognize it. so to answer your question, what made me think to do that is: experience!
sometimes one has to be shown what to do a few times before it sticks!
You're literally my savior. I have an exam today and my professor was crap at explaining everything, so I didn't understand any of the series and sequences. I watched at least 8 of your videos and they helped a lot! Thank you so much, Patrick!!
Patrick I love you! Your videos have helped me so much throughout calc 1 and now calc 2! Thank you for making these videos, so many of us appreciate it!!
you know you made it when you say "The answer is the number e"
e is a number though
Yeah, but stating e as the answer is more exact than saying 2.71 is the answer. For example, if for a problem you find the answer to be sqrt 2, it is much more accurate and precise to let the answer remain sqrt 2, even if you have been taught to simplify. This is because saying sqrt 2 = 1.41 is actually incorrect, even though sqrt 2 is approximately 1.41 if one is using three significant figures. So, you could indeed say the answer is approximately 1.41 (like if you are doing a physics problem where estimation>accuracy), and you would be technically correct, but it is much better to say sqrt 2. There is just no point in simplifying, it only takes more time to produce a crappier answer.
So, like +poopnuggets (lol) said: to answer e is to be exact, to name some number of digits of e is the answer is less exact. It is unnecessary to simplify, much like it is unnecessary to rationalize-- just more time and work for a less correct answer. I do not know how understanding an answer can be e is equivalent to "making it," but realizing that a concept like e is more exact than its estimated number is indeed helpful in math. Because, actually, e is not a number but a constant that can be expressed precisely as the base of the natural log (ln), such that ln(e)=1 (e^1=e), and can be estimated as the infinite series of 1/n!, which does not have an exact value since infinity is not a number either, just another concept, but does give us the estimation often used (2.71).
You can also do a lot of cool stuff with e that you cannot do with anything else (like its role in probability theory), and it has unique properties (such as the derivative of e^x is e^x, and the same applies for riemann integrals). ALSO, all digits of the constant e are not known (it is irrational), though the known number of digits is constantly increasing
series are really cool. it is one of my favorites subjects (if not my favorite subject) that one encounters in calculus. some very beautiful and useful results come from them.
of course, they are also pretty tricky at times!
@patrickJMT i like it when you go into the conceptual depths but at the same time keeping maths enjoyable, i feel really grateful to you., you just inspire me.....i like "improper integrals" in your video series very much :-)
I love the videos - they're so clear and really add to what I try to learn in class (we just go too quickly!)
Thanks for doing this!
God bless you dude! You have no idea how much these videos have helped me for my cal 2 final. the limit of my appreciation for your work approaches infinity. Great work!
thank you so much for being there i have been watching you videos for the whole day today about this topic..........they are very much easy to understand..thank you again!!
I would be so lost without you! I can honestly say I learned more over the course of watching your videos in one day than I learned the past 3 weeks in my Cal 2 class!
these videos are very much helpful i have been watching sequence and series topic for almost 8 hrs with small intervals and practicing problems in between ....i hope i will do well in exams
thank you so much ....people like you should always be there ....!!
just started studying this in calc II and your video was very helpful. sound quality was good and you made this topic less frightening!
Another few videos to once again get ready for yet another Calc 2 test. Thx Patrick you tht man.
good luck!
just so you know your the man. . .helped me through my calc II class with relative ease. Best vids on the net for sure.
Thank you so much for all your videos . Your videos have truely helped me.
1 to any real number power is 1.
the problem is if you have a function of the form [f(x)]^[g(x)] and f(x) is APPROACHING 1 (but not necessarily equal to 1).
limit notation is not very good; the standard notation is to use equality, when in reality it is just 'getting close' to that number (in most cases). eventually, one figures this out and just learns to deal with it : )
Thanks! I love how detailed you are. Keep it up!
So good man. Still helps people out after 11 years
i need to start paying you for all the nice ratings and comments : )
Bruh. If I pass my Calculus 2 exam. I’m so sending some cash your way and making a donation. You definitely deserve it! I’ve been using your videos since pre Cal. I don’t know where I’d be if it wasn’t for your videos. Thank you so much!😭
my pleasure my friend! hope the exam turns out well
i love you! thank you so much. ive been watching your videos all day for my final tomorrow. i think ill pass it because of you! :)
omg, thanks a ton patrick!! i have a maths exam next week, luv ur videos so much
Great video! I have a test on Tuesday and your videos have been so helpful.
I'd just like to let you know, though, that this video's not on your website.
Thanks again!
dude ur a lifesaver. Thank you for all this. You make so much easier
Your last example really helped me as I wondered if we would have to use the root test twice.
You did an excellent job! I only wish that I had discovered this while I was learning about this instead of after I had already finished the course.
However, I never really did understand it during the course, so I was lost during the assignment and exams, so this was like me learning it for the first time. However, my calculus teacher seemed to avoid doing examples or at least examples using numbers like you used.
Again, good job! I know others will benefit from it like I did.
glad to help it make sense for you!
6:12 "the numerator is going to get big quickly, the numerator is going to get big as well, but not as quick at the numerator"
lmao
lol
I'm looking like a dumbass laughing in the middle of the library right now...
Thank you so much!
I've been having trouble with Series! It'll certainly help my final today!!
Thank you helped a lot. Especially the last example!
For the 3rd question he did,
lim n->infinity (1+(1/n))^n is in fact equal to e.
Set y=(1+(1/n))^n, then take the natural log of both sides. You will have
ln y =n*ln(1+(1/n)) Then take the limit on both sides.
lim n->infinity lny = lim n-> infinity (n * ln(1+(1/n))
Now, the goal is to rewrite it in an indeterminate form in which the L'Hopital Rule can be applied easily.
lim n-> infinity [ln(1+(1/n)] / [1/n] which = 0/0.
Take the derivative on the numerator and denominator and you will be left with lim n-> infinity (1/ (1+(1/n))) and that limit will equal to 1.
Now we have lim n->infinity ln y = 1
lim n->infinity e^(lny)=e^1 and then replace y with y=(1+(1/n))^n after you cancel out e and the natural log. Therefore lim n->infinity (1+(1/n))^n = e
lim n->infinity (1-(1/n))^n is equal to 1/e.
thank you
...and btw... THANK YOU. Your instruction is fantastic. I'm so grateful to have found these videos.
I love seeing all of the steps. Thanks!
your videos are brilliant patrick, just brilliant :)
by the way, i wanted to ask if n-th term theorem could be used on your 3rd example here.
@patrickJMT no theres a place called jordan located in the middle east. You are making such a huge a positive feedback
thanks again my friend!!
@remirap no, i am long done with school.
Thank you for your videos! Everything is so clear.
Thank you so much for making this easy to understand! Fantastic.
ops, thanks!
i did that in another video too : )
i am making sure everyone is paying attention!
"most people seem to like them though" No No Patrick. Everybody LOVES them. You are a great man. Thousands of students around the world are more grateful than you know. Thank you for the time and effort you put into these videos. They have saved the lives of many students.
Awesome video dude, this helped me a ton thank you
thank you patrick. it really helps me a lot
Geez you make it much easier to understand than my professor...great stuff!!
but only the 1/n term goes to zero so that we are left with (3^0)(3^3) = 1(27) = 27
6:09 was pretty funny. :) thanks so much for the help though man. You have been a lifesaver.
Awesome video man. I definitely learned a lot.
Wow! incredible... especially the very last part of the root test!
it really helps me,thanks Patrick
You just saved my life man thank you so much
man youu are a LIFE SAVER !!! I wish u were my TEACHER !!!
THNX Matt ur Vids are the best!
Great lesson!
@armidylano44 well, i used to bore people at a major university as well, so maybe it is all the same
God bless you Patrick
Great videos, they are really helping my preps for the exams! By the way, at 5.45 you say that 0*27=27, not that it matters, the answer will still be the same.
no problem
wow. im at UT too.. and the whole time I wondered where patrick was at and it was right here.. same world!! Just show Austin rules!
YOU ROCK. I have a calc test this upcoming monday
@BornAtTheBar yep, got a masters
@patrickJMT
Hey, I noticed you're from Austin. I'm actually at UT right now =)
Anyway, thanks again. King of youtube math, you are.
I like how at 6:12 you referred to the numerator twice just to test if folks are paying attention. ;)
Those are fantastic questions. I would love to see a video just to have those answered. Is there a possibility of having this done?
i think you need to flip your fraction (n+1)/n
@5ANASHEEROA do you mean michael jordan? was he in the middle east?
I love how I got a video saying that videos from the 2000s math are not educational enough when this was a really good video.
excellent explanation, im getting to like this thanks to you
I thought series were going to be hard, but this whole concept so far, including doing differential eqtns with power series, and the Taylor polynomial section, has been easier than integration techniques IMO. First time in a while that I didn't actually need Patrick's videos to get it down correctly. Still watched them though, they always have something inventive to teach you.
thanks man, you absolutely rock!!!!
I LOVE YOUR TUTORIALS!!!! THANK YOU. I'M SO GONNA ACE MY CAL TEST!!!!!! :DDDDDD
@patrickJMT
Thanks for all your videos!! Its much easier for me to study math when I can pause and rewind the lecture :)
But I have a question, say I have a sum of (x/n)^n
what do I do with x?
at the end I got:
lim (x/n)
do I say that it converges for x
Great videos boss
woah, i never thought of that. thanks bud, this is gonna help with my exam i got tomorrow!
patrick you rock man
@BlueColourPencils awww, thanks! go texas!
I understand that if you have a function raised to the nth power, it is a good idea to use the root test. However, what about the other tests: integral test, sequence test, comparison test, and ratio test? What should you look for in a function to determine which of the other tests you should use?
You're my favorite teacher! =D
you sound like the hippie teacher on beavis and butthead. On a serious note your videos are very helpful. Thank you for posting!
Thank you sir
You rock, man. Better teacher than my Calculus professor. And I go to a major university too! =O
I know this is an over ten year old video but Patrick I hope you're having a good day
Sean Martin lmfao
OMG I agree with Inferfire........it is plain scary that I understand all your root test/ratio test stuff, I have my final tomorrow and before these videos I thought I was screwed because i have absolutely NO idea what my prof is babbling about....I wanna seriously thank you so much!!!
@Raxarax i was being a bit ' tongue in cheek ' with that comment
ahahahhaahah - that is awesome!
kisses + cookies = a good day
thank you for this video. YOU SAVED MY LIFE! :D
Thank you so much :)
due you mean why he raised it to the (1/n)? and if thats the question its because the equation has you find the limit of [an] to the nth root which is the same as raising the problem to (1/n). an example is the the square root of 4 which can be written as 4^(1/2). hope this helps :)
thanks a lot .... i helped me a lot
Amazing,, thanks a lot
Now i can tell okay, that..that.. Maths is Fun! all bcoz of Patrick!
For the last example on this video it is easier to use L'Hopitals on that limit by taking the ln of the limit instead of having to memorize that that limit equals e. You can show why it equals e.
I spent hours trying to understand my professor's instructions... yet I watched 3 of your videos, and I'm good to go. I've been barely passing Calc II, and not because I'm "dumb"... it's because I've spent an insane amount of time trying to understand HIS teaching. I should have sought other sources, and I would've done so much better in the class. I'm studying to be a teacher, and this really makes me see how there is NO "dumb" student... different students learn differently.
I'm not sure if this is an active conversation but if someone sees this please respond. In the proof of the Root Test I do not understand why you have to choose a q, Q