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.
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.
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.
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.
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.
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
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 🇮🇳
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.
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?
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
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!;)
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?
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 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
Oh man, this is waaaay easier than the book!
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
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 examples are always appropriate and clear.
Thanks, Snowball, I'm so glad the videos have been helping! :)
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
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
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.
Thank you so much, I even could understand how to get the sup and the inf via your video
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!
Your voice is so ASMR... I could fall asleep... Love it :)
first video i found which could explain it nice and easy. very well done!
+brovniemusic Thanks! Glad it could help.
Hey thanks for such a clear explanation! True grade saver!!!!
wow, this is literally perfect
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!
finally after lot of searches,got a quality explanation
keep going👍
Thanks, I'm so glad it helped!
You have very sweet voice and explain clearly . Thank You
Crystal clear! Thank you!
You're welcome! So glad it made sense!! 😊😊
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.
explained really well
Thank you from KSA
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!
well done . . once again excellent explanation. .
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!
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
thank you so much! This video help me understand the bounded sequences
you're welcome, i'm so glad it helped!!
I love you way of explaining calculus, you should apply for our uni instead of our teacher.
love u
Awesome explanation. Grasped it pretty quickly. Thanks!
And oh, your voice is just amazing,had to put that out
Have a good day :)
It's very clear... Can u please also answer this (-1)pwer n /n.. Please
How tf is your handwriting so perfect
Excellent explanation, thank you.
You're welcome, so glad it helped!
thank you so much this was what i've been looking
Awesome! Glad it could help.
perfect explanation. Thank You
Thanx a lot .you cleared my concept about this
You're welcome, I'm so glad it helped! :)
This video has helped me alot.
Thsnk you
You're welcome, I'm really 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!
Thank you soo much for this awesome explanation♥️
You're welcome Era, I'm happy to help! :D
Nice Bounded sequences
Tnku so much mam from india it's very useful ❤
You're welcome, I'm so glad it helped!! :D
a simple approach, thanks
You're welcome, Asare! :)
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 🇮🇳
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.
IT MAKES SENSE
Best explanation 👍👍👍👍👍 keep it up
Thanks for this lecture
You're welcome, Rupak! :D
This was really helpful. Thank you so much Krista( its your name right? ).
I wish you were my prof !
Great teaching! May i ask what app you are using ?
Thank you so much. You really helped me. Thanks
Glad it could help1
Easy to listen and understand:)
Nice explanation 😊
Thank you, Nazir! 🙂
Great explanation!! Thaanks
I directly subscribe to your channel
Thank yoooou Krista
+Saba Ali Thank you so much Saba!
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.
very nice,,, Helped a lot.
Thanks, Hassan! I'm so glad it helped! :)
you’re the homie
Ma'am could you please suggest some books on Mathematics which helps me to learn from the beginning of all maths concepts?
Super Useful, thank you!
You're welcome, I'm glad it helped!
I think I'm done searching Google for answers, hehe. :D
Awesome...great work
The easiest way ... Thnq
Thanks Ma'am.
You're welcome, Aishwarya! :)
Thank you! helped a lot :D
Sharmistha Saha You're welcome, I'm so glad it helped!
Thanks in a million!
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 )
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
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!;)
Top notch 👍👍👍
Nice vid, thanks.
Tqq.. It was easy to understand
You're welcome, Divya, I'm glad it made sense! :D
thanx a lot .. keep it up sis
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!
Love your voice
More than dat thank you
You're welcome, Kopano! :)
thank you, very helpful
+John Kaufmann Awesome, you're welcome!
The video is helpful
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?
Im using the stewart text and the second example is in the stewart :) hehe
Can i ask if the sequence is at first increasing so how can we found if it is bounded below or not. Tks Mrs.
helpful,thanks
Thank you so much!
+EsperanceBG You're welcome!
Thanks a ton! 🙏🏽
You're welcome, happy to help! :D
Thank you!!!
You're welcome, Syeda! :D
What if it was bounded above and not below, will it still be bounded?
Your vernacular and tone are seemingly identical to Salman Kahn. Interesting.
Thank you
You're welcome, Brandon! :)
You're welcome, Brandon! :)
U r the best
Wait. But can't n be 0, -1, -2 etc? It isn't really bounded from below right?
thank you so much
You're welcome! Glad I could help.
you just explain the things so perfect ...thanks really,🌹