Real Analysis | The Cauchy Condensation Test

[@henrique3194]

Real Analysis at saturday night 9PM. Great!

[@elgourmetdotcom]

I really enjoy all your analysis videos! Please keep posting! I would love one dedicated to Feynman’s technique seen rigorously but understandable 😊

[@IlayShriki]

Great video, simple to understand, you helped me a lot!

[@benedictkongyir1899]

I could not have asked for anything better. Thank you for blessing me with this video.

[@gh758]

why did you choose k

[@slavinojunepri7648]

Powerful stuff

[@goodplacetostop2973]

This video ∉ { Good places to stop }

[@blackbomber72]

:c

[@hoodedR]

😂😂

[@williamchurcher9645]

Surely it's this video does not contain good place to stop

[@yeech]

Hahahaha You are so funny

[@ramongallardocampos5241]

Analysis at 4 am I love it

[@3erBMW]

Thank you my drilla

[@MathPhys4U]

Love your traditional way of teaching the subject. I hope i can be as good as you.

[@zuggrr]

Fantastic explanation ! Thank you :)

[@sadececansu9]

nice explanation! !! I wonder why it is 2^n but e.g. not. 3^n ? Is it because it gives close terms I mean, like (a_4+a_5+a_6+a_7) ??

[@sirlight-ljij]

I bet this works for every monotonic N->N function f(n) like the following sum a_n converges sum (f(n+1)-f(n))*a_f(n) converges

[@davidpement]

At bare minimum, you need eventual nonconstancy, or else f(n+1)-f(n)=0, implying that every series converges. I don't know what other conditions you would need to impose.

[@jclopez5447]

I love your channel!

[@alicewyan]

Great videos! But please consider making the audio a bit louder, it's sometimes a struggle to hear them even at max volume

[@monkeydragnir3869]

I think it was your device

[@orenfivel6247]

The Cauchy Condensation Test's theorem can be proved by the integral test

[@shadowg5464]

Thank you for working it both ways! This is definitely gonna be on my test!

[@tianshugu9283]

The first person to prove harmonic series diverge was Nicole oresme, using the same method. And that result was not proved again for 300 years

[@tomatrix7525]

Love a bit of analysis at 3:51am

[@anatolyalikhanov9012]

What can you say about sum(r^n*a_{p^n}) ? Where r and p are integers.

[@radoonridoan7231]

Wait this had a name?

[@nevokrien95]

Can 2^n be switched by an arbitrery increasing integer sequnce ?

[@EquuleusPictor]

No, the increasing sequence must be slow growing: en.wikipedia.org/wiki/Cauchy_condensation_test

[@nevokrien95]

@@EquuleusPictor Slow growing is usually not an exponentiol. 😂

[@thesecondderivative8967]

​@@nevokrien95 It can. It's growing at an exponentially slow pace.

[@IustinThe_Human]

Does it work for all p integer numbers where you replace 2 with p? I this proof i haven't noticed a property of 2 that all natural number don't have.

[@thomasmagnuson5039]

Yes it does, it works for all positive integers. Proof is very similar to the one presented in the video

[@adarshyadav253]

I watch higher concept videos for entertainment