Real Analysis | The Cauchy Condensation Test

We prove a series convergence test known as the Cauchy condensation test. This test is motivated by the classic proof of the divergence of the harmonic series.

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[henrique]

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 😊

[benedictkongyir]

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

[IlayShriki]

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

[MathPhysU]

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

[gh]

why did you choose k<2^(m+1) in the contrapositive part of the proof?

[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

[alicewyan]

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

[tianshugu]

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

[shadowg]

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

[anatolyalikhanov]

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

[nevokrien]

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

[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.

[adarshyadav]

I watch higher concept videos for entertainment