Bounded sequences (KristaKingMath)

► 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
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QUORA // www.quora.com/profile/Krista-...

[@taifaldhuhli5546]

6 years ago and it is still way better than any other explanations❤️

[@kristakingmath]

I'm so glad it helped, Taif! :)

[@rahafalanzi.4352]

7 years ago and it is still way better than any other explanations❤️

[@pratappandey6751]

8 years ago and it is still way better than any other explanations❤

[@mukulraj2376]

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.

[@kristakingmath]

Thank you so much, I appreciate it! :)

[@proanimator.]

Simple, clear, and straightforward. What a breath of fresh air. Subscribed right away

[@helloworld4147]

Oh Geez! You just saved my one and half hour. Thanks a bunch.

[@maxguerra4155]

I can't tell you how helpful this was. Keep doing what you're doing!

[@kristakingmath]

Thanks Jordan!

[@moinaction]

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.

[@kristakingmath]

Aw thanks!

[@MadOrange644]

Oh man, this is waaaay easier than the book!

[@faraznahyan1768]

Your videos are very simple to understand, thanks a lot. It helped me finish my math assignments when I was completely lost haha

[@snsurabhi]

Thaaaanks a lot ma'am! This really helped a lot. Far more easily explained than many other videos. ❤

[@universegameplay21]

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.

[@bedof3470]

I don't know why the fuck professors don't explain concepts in easy ways as what I see in ths helpful vid

[@Folinic]

So true. Professors can make it so much harder than it has to be

[@RobbyBoy167]

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.

[@emki542]

you are the best tutor on this planet thanks for the master piece you nailed it ,,,,,welldone I

[@janed00]

Hey thanks for such a clear explanation! True grade saver!!!!

[@noirkenny]

wow, this is literally perfect

[@NaeemIrum]

well done . . once again excellent explanation. .

[@mustafaomer9578]

Thank you so much, I even could understand how to get the sup and the inf via your video

[@SaadDahiru-ri2fc]

Exactly now I get it sinceI’m searching for some videos about sequence but i couldn’t find it thank you so much ❤

[@kristakingmath]

You're welcome, so glad it helped! :)

[@kimberlycraft7129]

Fantastic explanation. Thanks so much!

[@rahulmore5254]

You have very sweet voice and explain clearly . Thank You

[@deepanshhh]

Awesome explanation. Grasped it pretty quickly. Thanks! And oh, your voice is just amazing,had to put that out Have a good day :)

[@brovniemusic]

first video i found which could explain it nice and easy. very well done!

[@kristakingmath]

+brovniemusic Thanks! Glad it could help.

[@pepsico815]

Thank you, explained it way easier than my textbook.

[@kristakingmath]

+Austin Texas You're welcome, glad I could help!

[@sohailnawaz8777]

what is example in which upper bound is present but lower bound is not present

[@nugget9245]

Your examples are always appropriate and clear.

[@kristakingmath]

Thanks, Snowball, I'm so glad the videos have been helping! :)

[@joshp6061]

explained really well

[@apderic1079]

perfect explanation. Thank You

[@KUNALMALAKAR]

It helps me a lot to understand the whole concept of the chapter,thanks...it was nice,specific and tactical...

[@kristakingmath]

I'm so glad it helped!

[@johnholme783]

Crystal clear! Thank you!

[@kristakingmath]

You're welcome! So glad it made sense!! 😊😊

[@azrinkmrdn3605]

i cant believe i finally understand this topic in just 12 mins.. thanks alot !

[@kristakingmath]

You're welcome, azrin, I'm so glad it made sense! :D

[@pureawesome01able]

thank you so much! This video help me understand the bounded sequences

[@kristakingmath]

you're welcome, i'm so glad it helped!!

[@Europa_Forever]

Your voice is so ASMR... I could fall asleep... Love it :)

[@liannascorner3679]

thank you so much this was what i've been looking

[@kristakingmath]

Awesome! Glad it could help.

[@johncoker7689]

Thank you so much!

[@Syvmana]

Thanks for making clear of what the bounded stuff means!!!!

[@kristakingmath]

Syvmana You're welcome, I'm glad I can help!

[@muskanangrish5001]

It's very clear... Can u please also answer this (-1)pwer n /n.. Please

[@shadyguru4201]

finally after lot of searches,got a quality explanation keep going👍

[@kristakingmath]

Thanks, I'm so glad it helped!

[@dalal1047]

Great explanation!! Thaanks

[@cklarenzcastro5827]

Great teaching! May i ask what app you are using ?

[@ramalingachary5318]

This video has helped me alot. Thsnk you

[@kristakingmath]

You're welcome, I'm really glad it helped!

[@mohd.arshad9088]

Awesome...great work

[@johng5295]

Thanks in a million!

[@dareal2669]

Thank you from KSA

[@slideIND]

thank you so much!!

[@nganoan2561]

Can i ask if the sequence is at first increasing so how can we found if it is bounded below or not. Tks Mrs.

[@tripti8186]

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?

[@bluemgc]

you're awesome! Thanks! you made me understand it in 12 mins! AWESOME!

[@kristakingmath]

bluemgc You're welcome, I'm so glad it helped!

[@lgtv8526]

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 ?

[@kevinle9249]

Thank you greatly!

[@chala0309]

Easy to listen and understand:)

[@ryancmf1]

Nice vid, thanks.

[@eramsaba8209]

Thank you soo much for this awesome explanation♥️

[@kristakingmath]

You're welcome Era, I'm happy to help! :D

[@saudisports]

Thank you so much. You really helped me. Thanks

[@kristakingmath]

Glad it could help1

[@KevaneeFagan]

May the good Lord bless you and your ability to explain. feel like a weight was removed off my back after watching this video.

[@Neueregel]

Nice Bounded sequences

[@abdulrahmanshaat3550]

I love you way of explaining calculus, you should apply for our uni instead of our teacher. love u

[@safiullahmahar1578]

Thanx a lot .you cleared my concept about this

[@kristakingmath]

You're welcome, I'm so glad it helped! :)

[@surendharloganathan5354]

Best explanation 👍👍👍👍👍 keep it up

[@drunkrussianisgood]

Excellent explanation, thank you.

[@kristakingmath]

You're welcome, so glad it helped!

[@360Science10]

Top notch 👍👍👍

[@caitlinm3719]

IT MAKES SENSE

[@hassanharoon923]

very nice,,, Helped a lot.

[@kristakingmath]

Thanks, Hassan! I'm so glad it helped! :)

[@Ricky_017]

Thanks for this lecture

[@kristakingmath]

You're welcome, Rupak! :D

[@saeedwiz]

thanx a lot .. keep it up sis

[@aishwaryar1998]

Ma'am could you please suggest some books on Mathematics which helps me to learn from the beginning of all maths concepts?

[@sharmisthasaha589]

Thank you! helped a lot :D

[@kristakingmath]

Sharmistha Saha You're welcome, I'm so glad it helped!

[@jiyuzeng3876]

helpful,thanks

[@nadeemqureshi8726]

You r awesome and especially your voice and the way you teach is seriously great. Thanks for the the video mam.

[@kristakingmath]

Glad you liked it!

[@zephyr1871]

you’re the homie

[@sattikbiswas2187]

This was really helpful. Thank you so much Krista( its your name right? ).

[@lanhikari1616]

Thanks a ton! 🙏🏽

[@kristakingmath]

You're welcome, happy to help! :D

[@onstaha2406]

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

[@syedamarjanarazzak5130]

Thank you!!!

[@kristakingmath]

You're welcome, Syeda! :D

[@cnifi69]

this was really hepful.. Thank you sooooooooooooooooooooo much

[@kristakingmath]

You're welcome, C! I'm so glad it helped!! :D

[@lgtv8526]

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

[@kristakingmath]

I'm so glad I was able to help! :D

[@coconut_punker]

can be increasing sequence monotonic?

[@KuldeepSingh-wo4yl]

The easiest way ... Thnq

[@TechVenturer]

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

[@asarerichmond7086]

a simple approach, thanks

[@kristakingmath]

You're welcome, Asare! :)

[@janewanjiru1396]

I wish you were my prof !

[@sebastarias]

really, really good explanation!! thank you very much for taking the time to explain this !!!

[@kristakingmath]

+Sebastian Arias Muños Glad you liked it! Thanks for letting me know.

[@dakota2386]

How tf is your handwriting so perfect

[@shoviksaha352]

What if it was bounded above and not below, will it still be bounded?

[@damangupta3765]

Tnku so much mam from india it's very useful ❤

[@kristakingmath]

You're welcome, I'm so glad it helped!! :D

[@AndrewSunx100]

What app do you use for pencast? I like this blackboard imitation!

[@kristakingmath]

Thanks, Andrew! I use Sketchbook with a Wacom tablet. :)

[@sabaal-yafie5529]

I directly subscribe to your channel Thank yoooou Krista

[@kristakingmath]

+Saba Ali Thank you so much Saba!

[@surajmedishetty2703]

Can you tell which type of software u are using to explain

[@kristakingmath]

Hey, Suraj! The blackboard program is Sketchbook by Autodesk. :)

[@aishwaryar1998]

Thanks Ma'am.

[@kristakingmath]

You're welcome, Aishwarya! :)

[@manishkushwaha8642]

The video is helpful

[@deepakvyas9571]

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 🇮🇳

[@hiteshvyas1]

appreciate your help saved my grades. thanks

[@kristakingmath]

I'm glad I could help!

[@YoYo-nt7yf]

Ikr i passed my 3rd semester because of her videos. AMAZING PROFESSOR TO ME🙋

[@nazirahmed99]

Nice explanation 😊

[@kristakingmath]

Thank you, Nazir! 🙂

[@FaresMYraj-ylol]

waw , great , thanks

[@andresstadelmann7583]

Am I right to assume that we can only plug in values that belong to the set of natural numbers (for sequences)?

[@betelhemdessie401]

+Andres Stadelmann Yes! since the domain of sequences is natural number.

[@andresstadelmann7583]

Betelhem Dessie Alright, great to know thanks!

[@divyabudime5507]

Tqq.. It was easy to understand

[@kristakingmath]

You're welcome, Divya, I'm glad it made sense! :D

[@tijubrain1]

Wish you were my Calc teacher!!! Awesome and clear explanation. Thank you!

[@kristakingmath]

+Sheikh Jobe Thank you very much! I'm so glad the video helped!

[@johnkaufmann8721]

thank you, very helpful

[@kristakingmath]

+John Kaufmann Awesome, you're welcome!

[@lightningrain2397]

Super Useful, thank you!

[@kristakingmath]

You're welcome, I'm glad it helped!

[@lightningrain2397]

I think I'm done searching Google for answers, hehe. :D

[@karina1810]

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?

[@mohammedalhaddar2182]

n tends to positive infinity since n is always a positive integer ( n>=1 )

[@AuditorMadness]

Wait. But can't n be 0, -1, -2 etc? It isn't really bounded from below right?

[@r3dmsl460]

I love you

[@kristakingmath]

You're welcome!

[@MathBySarah]

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.

[@kristakingmath]

+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.