Proof: Sequence (-1)^n Diverges | Real Analysis

[@Kevbotxd]

Watched this before my Real analysis midterm and this was one of the questions!!!! LETS GOOOO!!!!!

[@WrathofMath]

Nice!

[@Amira-x9r]

Thank you so much! I have been struggling in my Analysis classes but ever since I've found your channel everything is so much easier.

[@WrathofMath]

So glad to help! Good luck in your class and let me know if you ever have any questions! I am currently working on producing more analysis content!

[@nguyen9670]

Same

[@EgonuPatrick]

I had hopes of passing maths analysis but with you now am trying to gain confidence and am trying to understand things now

[@yashisingh6260]

.Thank u, my all doubts get solved with this wonderful lecture.

[@mahmoudalbahar1641]

Thank you for this good video.....you are cool mathematician .....keep going making great videos.

[@WrathofMath]

Thank you, Mahmoud! I will keep going!

[@kgopotsomasela4627]

7:16 can we set epilson to be a distance 0 < ε < 1??

[@rupsaseth2634]

We can take epsilon upto 0.9 or 9/10 but cannot take it as 1 cause for epsilon = 1, the intervals can have a common point 0 , which becomes the limit. We can say the limit does not exist or the function diverges as long as we do not have a common point between the 2 intervals, which in turn is possible when : interval 1 :- -1- 0. 9= -1. 9 to -1+0.9 = -0. 1 and interval 2:- 1-0.9 = 0.1 to 1+0.9 = 1.9 , where we have no common points between the intervals. It is basically possible if we take epsilon = 0.1, 0.2, 0.3,...., 0.9 .

[@bhanugupta7750]

Great video. Really appreciate it. They are very helpful. I think we can take any value for epsilon between -1 and 1 .

[@lalhriatpuiahmar5057]

But we say Epsilon greater than 0, so it can't be between - 1 & 0.

[@lalhriatpuiahmar5057]

Can we also use Epsilon = 1/3

[@wtt274]

Very clear explanation , thank you sir for this video !

[@WrathofMath]

Glad to help! Check out my analysis playlist for more and let me know if you have any questions! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli

[@turokg1578]

if i take two subsequences a_2n and a_(2n-1) since the two subsequences converge to different values can i say that it does not converge?

[@anonymousalias8818]

Are there any functions of x that use the basic 4 functions (addition, addition but negative, division, and division of divided numbers) that follows this pattern? Specifically I'm doing hijinks with (-1)^n toward a pattern of 3 that involve recursion, and I don't know a way to simplify powers of this when formulas including (-1)^n are in the power. As such, I'm looking for alternatives since all I need is a pattern where odds are all one constant and evens are all a different constant.

[@nancyliu8145]

|X(n)-X(n-1)|=|X(n)-A+A-X(n-1)|, which is smaller or equal to |Xn-A|+|X(n-1)-A |→0, so 2 is smaller or equal to 0.

[@maat6861]

Do you have a divergence proof example for trig functions, since they oscillate? For example sin(npi/2).

[@ismaelbiye1126]

Thank you. Very good explanation.

[@WrathofMath]

Thank you for watching!

[@nishant0312]

Is it an oscillatory

[@user-vn7ce5ig1z]

It doesn't converge to any number but it also doesn't diverge to +/-infinity, so what the heck does it diverge to? 😕

[@WrathofMath]

Nothing! Such is the nature of divergence. A divergent sequence is simply one that doesn't converge to any real number. Some of these happen to have the special property of "diverging to infinity" but others just oscillate!

[@user-vn7ce5ig1z]

@@WrathofMath Ah, okay, so a series that fluctuate back and forth between two or more values counts as "divergent"? I keep picturing the term as meaning it flys off _to_ somewhere. This makes sense now.

[@majoorbaghdad1672]

2n-(-1)^n, prove diverges?

[@Davivlcp]

Perfect

[@WrathofMath]

Thank you! Check out my analysis playlist for more and let me know if you have any questions! kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli

[@jacksonmadison9994]

That wasn’t so bad