Proof that the Sequence (-1)^n Diverges using the Definition

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God, you are life saver. Hope you will post more examples about diverge and converge

serinacat

Lol, using a contradiction can make life much easier lol. Great video :)

FPrimeHD

You should write a book and I will buy it. HaHa

serinacat

Life Saver - I looked all over for this proof

bricervantes

thank you! may you have a nice day and be safe. Us, first year collegemen are thankfull to you
^^

mandresyfalimanana

Hey big boy, you should put the title without the parentheses on "-1" otherwise it is near impossible to find your video

nicememe

"aha i have a CONTRADICTION. i can now prove what I need".

-> paraconsistent logic enters chat

GeekOverdose

(an
)n∈N = (-1)^(n+1) * (9/10) ^n How to find n ? and smallest an an∈(0, 1/100)

BB-fpce

What if you use less than or equal to epsilon definition

aislinnsmith

I don't really understand why there is a contradiction... If someone could explain me... thank you.

luciacherry

hey if we set up epsilon = 2 then we end up with a solution ie: -1 < L < 1. what causes this? cant we use epsilon=2. thnx for the proof... 😊

skitzobot

It doesn't diverge! (but it doesn't converge either)

OonHan

Why can you just remove the amount lines in the final inequality for each case?

vornamenachname

Or from 2:37 we could say that. -2<+L>0 wich is actually a contradiction itself and in that way just with this we know what we expected (convergent) is not posible. I am form Argentina so I can’t write it properly for sure but I wanted to know I’d that other way could be enough too. Very good the proof on this video ! Thanks :)

richardprofe

Thanks for the video, helped a lot, subscribed :)

danny

You proved the limit does not exist, but not if the limit diverges.

danieleferrara

Why not prove that for all L∈ℝ
there is some ε>0 such that for all N∈ℕ there is n∈ℕ such that n>N and |(-1)^n-L|≥ε. Wait this is the way to state that for all L∈ℝ (lim n->∞(-1)^n≠L) right? And proving this suffices to prove divergence of the sequences.

aneeshsrinivas

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