Bounded sequences (KristaKingMath)
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- เผยแพร่เมื่อ 24 ก.ย. 2024
- ► My Sequences & Series course: www.kristaking...
Learn how to determine whether or not a sequence is bounded. First you'll need to determine whether or not the sequence is monotonic, and if it is, whether or not it is increasing or decreasing. If the sequence is monotonic, then you can use your conclusion about whether it is increasing or decreasing to tell you whether it is bounded above and/or bounded below. You'll also need to take the limit of the sequence as n approaches infinity.
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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingm...
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6 years ago and it is still way better than any other explanations❤️
I'm so glad it helped, Taif! :)
7 years ago and it is still way better than any other explanations❤️
8 years ago and it is still way better than any other explanations❤
Extremely helpful. The hallmark of a great mathematician is to convey the magic of the subject as smoothly and in as simplified manner as possible. You did that job perfectly.
Thank you so much, I appreciate it! :)
Whenever I need to understand details bit by bit, I chose Krista King. Math couldn't get any easier the way she explains it. Thanks for doing what you the best.
Aw thanks!
Simple, clear, and straightforward. What a breath of fresh air. Subscribed right away
Oh man, this is waaaay easier than the book!
I can't tell you how helpful this was. Keep doing what you're doing!
Thanks Jordan!
Oh Geez! You just saved my one and half hour. Thanks a bunch.
I don't know why the fuck professors don't explain concepts in easy ways as what I see in ths helpful vid
So true. Professors can make it so much harder than it has to be
That's the tutors job I guess (actually teaching). Professors are just there to present a slide show presentation every class which students forget 90% of.
Your videos are very simple to understand, thanks a lot. It helped me finish my math assignments when I was completely lost haha
I would want my students to do more than just look at the first few terms to prove that a series is increasing/decreasing by either using the derivative of the function f(x) such that a_n = f(n) or by showing that a_n+1< a_n if decreasing and vice versa if increasing. If a student only showed that the function's first few terms had that trend, they could be tricked by one of those series that increased at first and then decreased or vice versa. Check this series out: a_n = (n-5)^2/10 + 10/n. Your method would make the student think that the sequence is decreasing monotonically when in fact it switches and starts to increase and has no limit as n -> oo.
+MathBySarah I agree! :) And I do teach that using the derivative to prove the series increases or decreases everywhere is the safest way to go. But sometimes, if it's simple enough, we can tell that the series is increasing or decreasing just by looking at it. And in that case, with these longer problems I'll skip that additional explanation.
This video explained everything. this is really great. I didn't even knew Monotone sequence. but with this explanation,now Ik both Bounded and monotone sequence and how to know that sequence is which one.
Thank you, explained it way easier than my textbook.
+Austin Texas You're welcome, glad I could help!
what is example in which upper bound is present but lower bound is not present
saw this video while giving the exam n scored a perfect score lol u 12 mins of teaching was better than my teachers 1 month long lectures
I'm so glad I was able to help! :D
you are the best tutor on this planet thanks for the master piece you nailed it ,,,,,welldone I
Thaaaanks a lot ma'am! This really helped a lot. Far more easily explained than many other videos. ❤
Your voice is so ASMR... I could fall asleep... Love it :)
Exactly now I get it sinceI’m searching for some videos about sequence but i couldn’t find it thank you so much ❤
You're welcome, so glad it helped! :)
i cant believe i finally understand this topic in just 12 mins.. thanks alot !
You're welcome, azrin, I'm so glad it made sense! :D
finally after lot of searches,got a quality explanation
keep going👍
Thanks, I'm so glad it helped!
Unfortunately, you are incorrect in couple of places. First, being bounded does not require monotonicity. As a matter of fact these two concept are separate. You might have a mono tonic sequence that is bounded or unbounded. A sequence could be bounded and not mono tonic, for example {sin(n)} is bounded and not monotonic. Second the graph of a sequence is not a continuous curve, just bunch of points on the plane.
Your examples are always appropriate and clear.
Thanks, Snowball, I'm so glad the videos have been helping! :)
Thank you so much, I even could understand how to get the sup and the inf via your video
Thanks for making clear of what the bounded stuff means!!!!
Syvmana You're welcome, I'm glad I can help!
wow, this is literally perfect
I'm not sure I follow your logic. It seems like you suggest that because it is non-monotonic, it cannot possibly be bounded, but I can still imagine a non-monotonic sequence that is bounded above and below... If all the positive values converged on a single point and all the negative values converged on another. It seems to be just a coincidence that there is no upper or lower limit in your example, totally unrelated monotonicity.
May the good Lord bless you and your ability to explain. feel like a weight was removed off my back after watching this video.
It helps me a lot to understand the whole concept of the chapter,thanks...it was nice,specific and tactical...
I'm so glad it helped!
Thank you from KSA
well done . . once again excellent explanation. .
first video i found which could explain it nice and easy. very well done!
+brovniemusic Thanks! Glad it could help.
extremely useful. i pay my professor thousands of dollars and explain shit and all that money doesnt buy me anything other than my pockets getting empty but your videos are great. keep posting. #respect #love
Hey thanks for such a clear explanation! True grade saver!!!!
Wish you were my Calc teacher!!! Awesome and clear explanation. Thank you!
+Sheikh Jobe Thank you very much! I'm so glad the video helped!
I love you way of explaining calculus, you should apply for our uni instead of our teacher.
love u
How tf is your handwriting so perfect
explained really well
You have very sweet voice and explain clearly . Thank You
Crystal clear! Thank you!
You're welcome! So glad it made sense!! 😊😊
thank you so much! This video help me understand the bounded sequences
you're welcome, i'm so glad it helped!!
so basically if a sequence is convergent then it is bounded n we can directly write it as bounded but for divergent sequences we have to do the whole brain storming ?
Any converging sequence is bounded.
To show that the second sequence is monotonically increasing you could consider the function y(x)=\frac{2x-3}{3x+4} for which y'(x)>0.
P.S. Greetings from Russia!;)
Wait. But can't n be 0, -1, -2 etc? It isn't really bounded from below right?
Nice Bounded sequences
you’re the homie
It's very clear... Can u please also answer this (-1)pwer n /n.. Please
IT MAKES SENSE
appreciate your help
saved my grades. thanks
I'm glad I could help!
Ikr i passed my 3rd semester because of her videos. AMAZING PROFESSOR TO ME🙋
Fantastic explanation. Thanks so much!
Awesome explanation. Grasped it pretty quickly. Thanks!
And oh, your voice is just amazing,had to put that out
Have a good day :)
You teach it so good... I understand it but I have a question that is What is difference between limit x approach 0 and upper bound............from India 🇮🇳
what happens if a(N+1) is defined in terms of a(N) and we are not provided the general a(N) sequence except the first term then how will i predict the sequence(a(N)) is convergent or not?
What if it was bounded above and not below, will it still be bounded?
But why didnt you use n=0 ,it produces a much smaller value than n=1 ?
This video has helped me alot.
Thsnk you
You're welcome, I'm really glad it helped!
Great teaching! May i ask what app you are using ?
All values n =N
But n=Z it is not below bound.
So how can you think n=N?
You r awesome and especially your voice and the way you teach is seriously great. Thanks for the the video mam.
Glad you liked it!
thank you so much this was what i've been looking
Awesome! Glad it could help.
Can i ask if the sequence is at first increasing so how can we found if it is bounded below or not. Tks Mrs.
If a sequence have upper bound then we call it limit of sequence or not
a simple approach, thanks
You're welcome, Asare! :)
I wish you were my prof !
really, really good explanation!! thank you very much for taking the time to explain this !!!
+Sebastian Arias Muños Glad you liked it! Thanks for letting me know.
This was really helpful. Thank you so much Krista( its your name right? ).
perfect explanation. Thank You
Thank you so much!
you're awesome! Thanks! you made me understand it in 12 mins! AWESOME!
bluemgc You're welcome, I'm so glad it helped!
Ma'am could you please suggest some books on Mathematics which helps me to learn from the beginning of all maths concepts?
Excellent explanation, thank you.
You're welcome, so glad it helped!
Hello Kristen please answer me
Alternating sequence like 1,-1,1,-1,
Is it dive but , why ?!
And it is monotonic or not ?!
Could you give me clear idea about alternating sequence
Please help me
Thanks for this lecture
You're welcome, Rupak! :D
Thanks Ma'am.
You're welcome, Aishwarya! :)
Thank you soo much for this awesome explanation♥️
You're welcome Era, I'm happy to help! :D
Thanx a lot .you cleared my concept about this
You're welcome, I'm so glad it helped! :)
Tnku so much mam from india it's very useful ❤
You're welcome, I'm so glad it helped!! :D
Thank you! helped a lot :D
Sharmistha Saha You're welcome, I'm so glad it helped!
If the sequence was decreasing monotonic, and the first term is the largest value thats its bounded above. Do you then find the value thats it bounded below by finding the limit as n tends to negative infinity? Or n tends to positive infinity?
n tends to positive infinity since n is always a positive integer ( n>=1 )
Thank you so much. You really helped me. Thanks
Glad it could help1
The easiest way ... Thnq
can be increasing sequence monotonic?
Thanks in a million!
Great explanation!! Thaanks
Nice explanation 😊
Thank you, Nazir! 🙂
Easy to listen and understand:)
I directly subscribe to your channel
Thank yoooou Krista
+Saba Ali Thank you so much Saba!
Your vernacular and tone are seemingly identical to Salman Kahn. Interesting.
Nice vid, thanks.
Best explanation 👍👍👍👍👍 keep it up
Top notch 👍👍👍
helpful,thanks
Awesome...great work
very nice,,, Helped a lot.
Thanks, Hassan! I'm so glad it helped! :)
Thanks a ton! 🙏🏽
You're welcome, happy to help! :D
The video is helpful
Thank you!!!
You're welcome, Syeda! :D
thanx a lot .. keep it up sis
Thank you
You're welcome, Brandon! :)
You're welcome, Brandon! :)
Am I right to assume that we can only plug in values that belong to the set of natural numbers (for sequences)?
+Andres Stadelmann Yes! since the domain of sequences is natural number.
Betelhem Dessie Alright, great to know thanks!
Tqq.. It was easy to understand
You're welcome, Divya, I'm glad it made sense! :D
waw , great , thanks