Proof: Sequence (3n+1)/(n+2) Converges to 3 | Real Analysis

We prove the sequence 3n+1/n+2 converges to a limit of 3 using the epsilon definition of the limit of a sequence. #realanalysis
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Real Analysis Course: • Real Analysis
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[@WrathofMath]

Support the production of this course by joining Wrath of Math to access exclusive and early videos, original music, plus the real analysis lecture notes at the premium tier! kzbin.info/door/yEKvaxi8mt9FMc62MHcliwjoin Real Analysis course: kzbin.info/aero/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli Real Analysis exercises: kzbin.info/aero/PLztBpqftvzxXAN05Gm3iNmpz9SkVfLNqC

[@callme_lyds]

This is the most clear explanation on KZbin, thank you!

[@colehillyer7284]

Thank you. You make the purpose of every step clear which makes this much easier to follow than my textbook.

[@WrathofMath]

Happy to help!

[@karolinazajac4668]

The condition for N doesn't include the fact that N has to be a natural number

[@oderoivan]

Well explained

[@explorewithshuaib2372]

Thanks love from india

[@WrathofMath]

Glad to help! Thanks for watching and let me know if you ever have any questions!

[@explorewithshuaib2372]

@@WrathofMath Yeah sure I have a question I can send you a picture of that question, could you please provide me your email?

[@WrathofMath]

No promise I'll be able to respond, but you can try messaging it to me on Instagram! Check my profile for the link.

[@yolandasithole5072]

Thank you. I struggled for years

[@WrathofMath]

Glad to help, thanks for watching!

[@henrywoo1668]

Thank you sir for this great video.Your explanation is so clear that a fool like me can understand nevertheless. Flow of ideas coupled with explanations are coherent and logical that no details are missed .Happy New Year !

[@WrathofMath]

Thank you Henry! Happy new year!

[@thembumenzimthokozisindlan9917]

I don't usually leave comments. You know what, big up yourself man!!!!

[@empirestudio3024]

Please solve this Lim n-->infinity (2n-3)/(n+1)=2 Love from india✨

[@Maya-fe8xm]

Hello! Is it okay that N is negative when epsilon is greater than 5/2? Thank you.

[@Maya-fe8xm]

or since N must be a natural number is it the case that epsilon cannot be greater than 5/2

[@ArchanaSubramani]

Hi for this question I don't understand why my professor is doing this method? mn→∞6n/(2n−7)= 3. Proof Letε >0 be arbitrary.Take N=[21ε]+ 14, so 21/N< εand 2N−7≥N.Letn≥N be arbitrary.Then|6n/(2n−7)−3|=|6n−(6n−21)/2n−7|=|−21/2n−7|=21/2n−7≤21/2N−7≤21/N< ε.

[@ArchanaSubramani]

but your method makes more sense would it be still correct

[@BilalTaskin-om6il]

Hi. Thank you so much. You are really a life saver. Could you add records (like sequences) for continuity and especially differentiability? I really appreciate your effort and help. Thank you so much.

[@WrathofMath]

Thanks for watching! If you look at my Real Analysis playlist, I have several continuity proofs. Differentiability will come, I'm looking forward to making those videos! But there is a lot of material to cover.

[@tanusreekar2839]

thank you! saved me

[@WrathofMath]

Glad to help, thanks for watching!

[@robertvaughn3554]

Very well organized

[@WrathofMath]

Thank you!

[@nosir1479]

I love you

[@victorthaler9495]

is the following correct? choose n_0 > 5/e then for all n > n_0 ... 5/(n+2) < 5/n < 5/n_0 < 5/(5/e) = e

[@finnpayton2173]

lol two months later: Yes

[@AntonyK_]

Why didn’t you take away +2? I had a similar question in class, and my prof said this way isn’t correct, so I just want to see why it’s better to take away any constant out

[@WrathofMath]

I don't understand your question, could you rephrase?

[@AntonyK_]

@@WrathofMath from your question, can we make N=5/epsilon instead of 5/epsilon -2? Then, in the pf. Can we make 5/N +2 < 5/N = 5/5/epsilon = epsilon? Because I had a similar question in class, and the prof said sth like we can’t make N= sth + or - a constant all the time, which I don’t completely understand what he’s saying.

[@Ryan-mw4zv]

@@AntonyK_this is a great point!! I did a similar attempt and got final result 10/n > 0 st n is a natural (positive integer). i believe this is using the archimedean principle but i am not sure?

[@like_that4966]

thanks a lot! i don't even need to buy a textbook now.

[@WrathofMath]

Glad I could help!

[@alivemuch6265]

THANK YOU!!!

[@WrathofMath]

You're welcome!

[@P0pper]

youre the goat

[@Eis461]

Thank you

[@itscurious_ks]

Lovely man thx

[@WrathofMath]

Glad to help!

[@KaouTa-n8g]

Can u prove this one with the same method cuz i found it hard . Prove the following: (a) lim (−1)^n÷n n = 0

[@jizert]

as n approaches?

[@angelaberkies8615]

You are so Cute

[@NajwaOlo-d9h]

😂😂😂😂😂😂😂you’re just killing me , this is why you’re not understanding what you’re reading 😂