series

[gilded tree]

How to solve this question? I trued to seperate an+1

[spice coyote]

Notice that if u want to show it’s not bounded u can choose a lower bound. Also notice a_n >= 0 obv

[gilded tree]

But how to check it

Please teach me. I want to learn it

[spice coyote]

Actually mb

I just noticed that I made it an upper bound

Notice that $a_n = a_{n-1}$ for $a_n = 3$

[flint carbon]

Dappiest Dog Dappina

[spice coyote]

It’s trivial from there

[north badger]

How is it trivial

Who said it will ever equal 3

[spice coyote]

Bruh

Pyro

U stupi

If it goes above it will fall back

If it’s below it will go up

Obv it will converge to 3 then

[north badger]

Who's saying that

You? Lmao

There are conditions for convergence to a fixed point

You didn't verify anything

[spice coyote]

U gotta be trolling

There are easy lemmas for this

One can prove them literally with calculus knowledge

[north badger]

Dappy, stop and get help

If you have a lemma or whatevershit, you have to state it

Not everyone cares enough to know about this stuff

Stop saying obv

It's really not helping you mathematically

As a certified human being, it is not at all obvious to me why the sequence should converge to 3

And I can probably very easily construct a similar example that does NOT converge

[spice coyote]

Go ahead

Construct a similar example with that condition meet, yet doesn’t converge

U can’t

They all look like this

[north badger]

What condition

[spice coyote]

Well it should be obv that u can’t just pull sin and e out of ur ass

This is a special form

It’s not a polynomial and I don’t know the official name but I think u know what I mean

[north badger]

Talking to you is like decrypting with brute force

You have such a ridiculous way of talking about math

Anyway

[spice coyote]

I gtg

I will wait for that example

[north badger]

Forget about the example

Tell me why it converges

That's all

[spice coyote]

Look at this

It’s a n to a n+1

If it goes above it will go below

If it goes below it will go above

[spice coyote]

Therefore if such an exists

It must converge to it

The only Argument u could bring is a cycle

[north badger]

That is not a proof

[spice coyote]

But that doesn't matter

Since a cycle is bounded

[north badger]

This is roughly the result I know

[spice coyote]

And it doesn't do a cycle either

[spice coyote]

Ofc it isn't I never said it is

It's the intuition

[north badger]

Who cares what you have to say then

If it's not a proof

[spice coyote]

The author asked if it's bounded and how to prove it

I gave him the answer to the first question and important intuition for problems like tjst

At least I hope I did

[north badger]

Did you prove its bounded

I can't see where

First you said it's trivial

Then you said it must converge

Then not so sure it converges

But if it doesn't its a cycle (no idea why?)

I hope you start actually doing math one day

That would be epic

[spice coyote]

I hope u one day reach my level so u can start to understand me

Would be great

[north badger]

The reason you're hard to understand is not because you're too good

I am 100% for real

Communication is one of your weakest points

And you tend not to justify your statements, and being correct does not excuse your handwavy approaches

In short, excuse rejected, get better

[spice coyote]

It's discord

Like I am actually gonna elaborate

I gave a hint

Maybe it will help maybe it won't

[gilded tree]

I asked the question and you guys are not talking related to the question. You can move to other channels for chat

[spice coyote]

I wanted to help u, pyro just wanted to shit on me, I'm sorry

[gilded tree]

It's okay. You can give me advice right now. How to solve this

[spice coyote]

There are several ways to approach this after the hint that I gave u

Idk how experienced u are so I'm just gonna advice u to do the simplest one

For that simply show that [0,3] maps to [0,3] using derivatives

[gilded tree]

What do you mean maps to this?

I'm learning English too so maybe my bad

[spice coyote]

Well if u solve for a n+1 u have a function from a n to a n+1

If u show that any a n in 0 3 is mapped to another a n+1 in 0 3 u are done

[gilded tree]

Can you suggest any youtube video related to it?

[north badger]

It is actually related, believe it or not

[north badger]

I'm not just shitting on him. Does it not bother you that he keeps saying trivial and obviously every other message when he hasn't even provided an answer to your question?

[spice coyote]

Pyro just bcs u don't find it trivial don't hate me for it