Limit Comparison Test Proof

In this video, I prove the famous Limit Comparison Test to determine the convergence or divergence of a series. I also state and prove a related version, called the Limsup Comparison Test. Enjoy!

[ugursoydan]

thank you very much a siple but very benefitful proof

[tgx]

There is second way (N^3-1)/(N^4+1)>= (N^3-N^2)/(2*N^4)=(N-1)/(2*N^2), but series (N-1)/N^2 is divergent, we can use Bolzano Cauchy, there is ((N+1)-1)/(N+1)^2 (N/(N+N)^2) *N>=1/4

[mauri]

Hello prof peyam, u are very very good to teach!! Congratulation u are really good teacher. If possible i want to ask u some doubts that I have and I hope u will explain in this channel. I never found the proves of this concepts:
1)why the rotor operator means a rotation;
2) the meaning of divergence and the proof;
3) the proof of meaning of variance and convolution in probability;
Thank u very much
Maurizio

[ChandanDas-wyyl]

Sir, please upload limit sup and limit inf conceptual video

[cauchy]

But what I know that if lim an =0 when n-->+oo the series is cnverge