What is a Sequence? Examples showing convergence and divergence of sequence.
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- Опубліковано 19 жов 2024
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Hello patrickJMT.I just want to say "Thank you" and say ""peace be upon you" for sharing your knowledge from Adana,Turkey.
vay :)
you have seriously gotten me through calc 1 and now through calc 2, you're the only tutor who makes sense!!!!
DUDE YOU'RE THE MOST AMAZING GUY EVER!!!!!!!!!!!!!
If you think so, then watch "physics wallah " But he speak hindi so i think that you can't understand him, but i want you to believe that he is the real great
Patrick is love, Patrick is life
thank you very very very much patrick ......you are the best tutor that i have ever seen in my live......you helped me a lot ..........i wish that i can help you something in return ............
To dumb down for people who didnt understand: 1. Take the limit of the sequence. 2. Does the limit exist? (0 or any other integers like 2, 4, 328, etc.) If so it converges to that value. 3. If it doesn't exist then it is divergent. (Positive infinity, negative infinity, DNE from most trig functions, etc.)
Left handed sob you learned me calculus I & II just because of your videos
much thanks
so when it goes to infinity it diverges but when it is pretty much going to 0 it converges ?
3^n increases faster than 2^n. Therefore, as n aproaches infinity, the denominator is much larger than the numerator. Ex. 1/1 000 000 000 000 000 000 = 0 (aprox).
Thank you bro! keep up the "good work"! :)
Thank you so much! Your explanations are so helpful.
incredible teaching mr.patrick
ferit abi nasisin?
saolasan sen nasılsan
After Patrick helped me in highschool maths, I am here again for college calculus LMAO.
why is your volume always so low? i have my volume maxed out and i can barely hear you
Right
Great tutoring man!
you're amazing! thank you LOADS!
You're great.
I agree.
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This is very helpful !!!!!!!!!!!
Thank you sir!
I am not going lesson because of you :) thank you so much
ur awesome-Anything i need i goto youtube and look for your hands :)
Is it possible to have a sequence without pattern?
Tnx for explaination
Haha I was like 0 times 1/3 equals 1/3
That's right answer
been there bro
Thanks for the help bro
thank you for helping me 😢
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You are awesome!!
Keep going✌
tq soo much bro
@yahya3563 just tell your friends and keep watching :)
You cant add/subtract, but it is totally possible to multiple infinity x infinity which gives infinity.
why (2/3)^n is 0. Can you please explain that.
+HUAYCAPAC it's lim(2/3)^n as n approaches infinity, and it equals 0.
Take 2/3 of 1. That is 2/3.
Then take 2/3 of 2/3. Then take 2/3 of 2/3 of 2/3. You'll eventually get numbers close to 0.
you are the best
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Thanks bro🥰
legend
patrick I have problem with how to write recursive formula and explicit formula for a sequence ??
What if the value inside the bracket (in the last example) is exactly -1?
Thanks, i was so confused whats converges and diverges mean
thx, help a lot. Im just gonna have a midterm about cv and dv later in 2 hours.
where did the 0 come from at 10:53?
Imagine graphing f(n) = (2/3)^n. Remember: Limits are to answer the question "what happens to f(n) as n approaches a number?" In this case, what happens to f(n) as n approaches infinity? Since 2/3 is less than 1, the graph approaches f(n) = 0, so the limit is 0.
nice sir👌👌👌
how is the 2/3 = 0 ??
in the second example
A book on Meterology brought me here.. Am I watching the wrong video lol.. I was studying the formation of air particles... This is unrelated to my book
+Mase Money glad you liked the video!
Patrick I understand
in my class you can´t use l´hospital with "n" numbers because the theorem is proven for continual function. and differentiable function. and is not the case with natural numbers. so first you need to change the variable to "x" with x being a real number. I know in practice is almost the same. but its mathematically incorrect doing directly.
same
which rule is that
NICE
8:08 multiplying infinity by infinity?
10:52 so 1/3 × 0 = 1/3 ,, how
1/3 * 0 = 0 not 1/3
1/3 times 0 is not 1/3 it’s 0??
I suspect you saying that theorem for less than or equals ,i.e., anything in the bracket there must lie in -1 to 1
I think it must be less than only since 1 power infinite non sense !
Is there a specific cases when if any equation is diverges or converges ?
Thanks ..
Hello Gr.10 students😁
how come (2/3)^n = 0 ?
+YAHOO because darude sandstorm
+YAHOO if 0 < k < 1 k^inf = 0, if k > 1 k^inf = inf.
If k = 1... well it's a difficult question. It depends. Negative k is undefined.
unfortunately youtube doesn't allow to write formulas properly so google "exponential limits".
+YAHOO
Graph f(n) = (2/3)^n. This exponential function approaches 0 as n approaches infinity. Thus, the limit is 0.
Remember: the general form of exponential is f(n) = a(r)^n) is greater than 1 or less than 1, then the graph goes UP, but if it is between 1 and -1, the graph goes DOWN to 0
Because when you multiply a fraction less than 1 by itself it just keeps getting smaller and smaller and approaches 0. For example, lets say we have a sequence (1/2)^n. The first few terms would be: 1/2 + 1/4 + 1/8.... For (2/3)^n the first few terms would be would be: 2/3 + 4/9 + 8/27....
How 1/3.0 =1/3 plz anyone
mistake at 11:00. 1/3 * 0 is 0. he accidentally wrote 1/3
not even 10 seconds later he fixes it...
thank you for validating this. I was a bit thrown off at first :-p
Wait a second - why is 1/3*0=1/3?
Continue watching till the end to see why
@@Rayan-yg1pk lol
♥️🙏
sir tecson
Or maybe he is ESL.
lol same here