Bounded sequences (KristaKingMath)
ฝัง
- เผยแพร่เมื่อ 22 ก.พ. 2014
- ► My Sequences & Series course: www.kristakingmath.com/sequen...
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.
● ● ● GET EXTRA HELP ● ● ●
If you could use some extra help with your math class, then check out Krista’s website // www.kristakingmath.com
● ● ● CONNECT WITH KRISTA ● ● ●
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.kristakingmath.com
FACEBOOK // / kristakingmath
TWITTER // / kristakingmath
INSTAGRAM // / kristakingmath
PINTEREST // / kristakingmath
GOOGLE+ // plus.google.com/+Integralcalc/
QUORA // www.quora.com/profile/Krista-...
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!
Oh Geez! You just saved my one and half hour. Thanks a bunch.
I can't tell you how helpful this was. Keep doing what you're doing!
Thanks Jordan!
Your videos are very simple to understand, thanks a lot. It helped me finish my math assignments when I was completely lost haha
Thaaaanks a lot ma'am! This really helped a lot. Far more easily explained than many other videos. ❤
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.
Hey thanks for such a clear explanation! True grade saver!!!!
Fantastic explanation. Thanks so much!
Thank you so much, I even could understand how to get the sup and the inf via your video
wow, this is literally perfect
well done . . once again excellent explanation. .
you are the best tutor on this planet thanks for the master piece you nailed it ,,,,,welldone I
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.
You have very sweet voice and explain clearly . Thank You
perfect explanation. Thank You
Your examples are always appropriate and clear.
Thanks, Snowball, I'm so glad the videos have been helping! :)
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
first video i found which could explain it nice and easy. very well done!
+brovniemusic Thanks! Glad it could help.
Crystal clear! Thank you!
You're welcome! So glad it made sense!! 😊😊
explained really well
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! :)
thank you so much this was what i've been looking
Awesome! Glad it could help.
Thank you 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 :)
thank you so much! This video help me understand the bounded sequences
you're welcome, i'm so glad it helped!!
Thanks for making clear of what the bounded stuff means!!!!
Syvmana You're welcome, I'm glad I can help!
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.
Great explanation!! Thaanks
Thank you greatly!
Your voice is so ASMR... I could fall asleep... Love it :)
Awesome...great work
This video has helped me alot.
Thsnk you
You're welcome, I'm really glad it helped!
Thank you from KSA
Thanks in a million!
thank you so much!!
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!
finally after lot of searches,got a quality explanation
keep going👍
Thanks, I'm so glad it helped!
you're awesome! Thanks! you made me understand it in 12 mins! AWESOME!
bluemgc You're welcome, I'm 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
Excellent explanation, thank you.
You're welcome, so glad it helped!
Easy to listen and understand:)
Nice vid, thanks.
Thank you so much. You really helped me. Thanks
Glad it could help1
Thanks for this lecture
You're welcome, Rupak! :D
Thanx a lot .you cleared my concept about this
You're welcome, I'm so glad it helped! :)
Thank you soo much for this awesome explanation♥️
You're welcome Era, I'm happy to help! :D
Great teaching! May i ask what app you are using ?
very nice,,, Helped a lot.
Thanks, Hassan! I'm so glad it helped! :)
helpful,thanks
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?
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 ?
Thank you! helped a lot :D
Sharmistha Saha You're welcome, I'm so glad it helped!
thanx a lot .. keep it up sis
a simple approach, thanks
You're welcome, Asare! :)
Thank you!!!
You're welcome, Syeda! :D
It's very clear... Can u please also answer this (-1)pwer n /n.. Please
Thanks a ton! 🙏🏽
You're welcome, happy to help! :D
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!
Nice Bounded sequences
IT MAKES SENSE
Top notch 👍👍👍
Best explanation 👍👍👍👍👍 keep it up
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🙋
May the good Lord bless you and your ability to explain. feel like a weight was removed off my back after watching this video.
Thanks Ma'am.
You're welcome, Aishwarya! :)
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.
The easiest way ... Thnq
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!
Can i ask if the sequence is at first increasing so how can we found if it is bounded below or not. Tks Mrs.
Super Useful, thank you!
You're welcome, I'm glad it helped!
I think I'm done searching Google for answers, hehe. :D
thank you, very helpful
+John Kaufmann Awesome, you're welcome!
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
I directly subscribe to your channel
Thank yoooou Krista
+Saba Ali Thank you so much Saba!
this was really hepful.. Thank you sooooooooooooooooooooo much
You're welcome, C! I'm so glad it helped!! :D
This was really helpful. Thank you so much Krista( its your name right? ).
Nice explanation 😊
Thank you, Nazir! 🙂
waw , great , thanks
Tnku so much mam from india it's very useful ❤
You're welcome, I'm so glad it helped!! :D
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
The video is helpful
How tf is your handwriting so perfect
Wait. But can't n be 0, -1, -2 etc? It isn't really bounded from below right?
I love you way of explaining calculus, you should apply for our uni instead of our teacher.
love u
Ma'am could you please suggest some books on Mathematics which helps me to learn from the beginning of all maths concepts?
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
Tqq.. It was easy to understand
You're welcome, Divya, I'm glad it made sense! :D
What if it was bounded above and not below, will it still be bounded?
awesome thank you!
Glad it could help!
you’re the homie
can be increasing sequence monotonic?
thanks easy to undertsand briiliant :)
I wish you were my prof !
Love your voice
More than dat thank you
You're welcome, Kopano! :)
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 app do you use for pencast? I like this blackboard imitation!
Thanks, Andrew! I use Sketchbook with a Wacom tablet. :)
thank you so much
You're welcome! Glad I could help.
you just explain the things so perfect ...thanks really,🌹