Intro to Sequences | Calculus, Real Analysis
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- čas přidán 26. 08. 2024
- We introduce sequences, consider them as functions, and go over some sequence notation as well as other concepts and terminology in today's lesson video lesson on sequences!
A sequence is a list of numbers in some definite order. Each number in a sequence is called a term of the sequence. So the first number in the sequence is the first term. Some sequences have nice expressions that tell us how to find the nth term in the sequence, but not all sequences are so simple. We'll touch on the Fibonacci sequence as well, which is an example of what's called a recursive sequence.
If a sequence gets arbitrarily close to some real number, we call that number the limit of the sequence and say the sequence converges to the limit, and thus the sequence is called a convergent sequence. A sequence that doesn't converge is said to diverge. A sequence may diverge to positive infinity, negative infinity, or neither. For example, the sequence s_n = (-1)^n is -1, 1, -1, 1, ... . This sequence doesn't converge - so it diverges, but not to positive or negative infinity.
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This really helped. I had to skip the class for this because of a lack of planning. You jumped my gap.
Glad to hear it, thanks a lot for watching! If you're looking for more real analysis, check out my playlist: czcams.com/play/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli.html
This guy is a life saver. Thanks a lot, I think I am gonna pass LA this semester
Glad to help - good luck!
Best tutorial for Infinite sequence. Thanks alot
Glad to help! Thanks for watching!
OMG, this video is so useful!!!!!
Glad to hear it, thanks for watching! Check out my Real Analysis playlist if you haven't already, much more to come! czcams.com/play/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli.html
Thank you so much. This helps so much
Glad to hear it, thanks for watching!
thank you it helped SO MUCH!!!
Great !
Thank you!
Many thanks for this good video.
Really helpful
Glad to hear it, thanks for watching!
how can i make a formula from this kind of sequence:0,1,0,1/2,0,1/3,0,1/4...
thank you very much!
Glad to help, thanks for watching and let me know if you have any questions on real analysis stuff - more lesson on the way!
Does sequence need to have a specific rule to define all the terms,
What i mean is, if i write random numbers, no rule, no order, would it be considered a sequence? {2,56,5,43,5,,67,89,.....}
No it won't be considered a sequence
If should be ordered
Wow you already have an upload
Exactly!
Haha, there’s no time to waste! Thanks for watching, Keith! Also, after a good night of sleep, I think I see what I was missing with your problem last night. I thought there was an error in the question because it said all four digit numbers divisible by 2^a * 3^b * 5^c are made up of the digits 0, 2, 3, and 7, however we can find several four digit numbers divisible by factors of 2, 3, and 5, that are not made of those digits. I was mistaken about a, b, and c. I thought they could be any positive integer, I think the question is restricting us specifically to values of a, b, and c, such that the product of 2^a * 3^b * 5^c is a factor of some four digit number that IS made of the digits 0, 2, 3, and 7. With that in mind, the problem is certainly tricky and I’m not sure exactly how I’d solve it at the moment, but I hope that brings some more clarity! Let me know if you’re not sure what I mean!
@@WrathofMath Thank You!!! Btw, when are you going live again?
No problem! I'm travelling out of state tomorrow and Saturday morning, so I'll probably stream Saturday night or Sunday night. I'll post it on the community tab when I decide. Hope to see you there!
@@WrathofMath I'll try
Thank you!
You're welcome! Thanks for watching and let me know if you ever have any video requests!
really helped thx. new sub :)
Glad to hear it, thanks for watching!
At first thanks a lot for this video! I wonder sequence is simplified....
I have question in this topic
-You have written a sequence Sn=n and told that it's diverges....my question is do the sequence Sn have any limit? And if there is any what's that?
Thanks for watching and are you asking specifically about the sequence Sn=n of natural numbers? For this one, we may say (and write) its limit is positive infinity. You may also hear people say its limit simply doesn't exist. It has no finite/real limit. Check out my analysis playlist if you're looking for more!
czcams.com/play/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli.html
@@WrathofMath Thanks a lot!
If a sequence diverges, it has no limit (or its limit is infinity) but if a sequence converges, that means it has some boundaries.
keep teaching
😀😃😄😁
Thank you, I will!
Love from 🇮🇳. Can you write your content in an order so we can note that.
Thanks for watching! Do you mean to indicate which order my videos should be watched in? This video is part of my growing real analysis playlist: czcams.com/play/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli.html
Still a long ways to go, but it is just over 60 videos currently.
@@WrathofMath no sir,i doesn't mean that .i mean that roughly write on screen in this particular video. I watched your other video. In that it is fine.
I'm learning this and have a question. What would you say if I were to write of the final exercise:
n+2/-5^n (-1)
Maybe it's kind of stupid but it would work, right?
Love from 🇮🇳..pls make video on IIT JEE MATHS
He doesn't know what JEE is, he is foreigner 😂
Ooh yes!! 😄
Oh yes indeed :D Thanks for watching!
sorry,nothing i understand