Proof: Sequence 1/n Converges to 0 | Real Analysis Exercises

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We will prove the sequence 1/n converges to 0. In other words, we're proving that the limit of 1/n as n approaches infinity is 0. We use the epsilon definition of a convergent sequence and the proof is straightforward, following the typical form of a convergent sequence proof and using the Archimedean Principle. #RealAnalysis

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Already did this class but still watching. Your way of explaining is amazing

ChocolateMilkCultLeader

Really short and sweet. I can do vector calculus but still struggle to understand how to tell when something is divergent or convergent, but this helps. Thanks for the lesson, I enjoyed it.

cmdrbobert

Thx for proving, but according to the definition, we should set N as an integer. And we should set N = [1/epsilon] + 1 to ensure that N is an integer.

Momo_SuperCool_

Out of curiosity just thought to raise this query - the sequence where nth term= 1/n is convergent becoz of the basic definition of convergence as lim n->infinity (1/n) = 0 as explained on this video but the harmonic series -- 1+1/2+1/3 + ••••••+1/n +...where general term is 1/n is divergent due to P series test logic. Any thought?

subrotobanerjee

Thanks Sean, another top notch lesson.

rmw

1st!! thanks for these joyful moments really appreciate it!

aashsyed

Do you have any tips for understanding proofs?

samsonlawal

Do you have a proof of the comparison theorem which states that: Suppose that (an) and
(bn) are convergent sequences, and that an ≤ bn for all n ∈ N. Then limn→∞ an ≤ limn→∞ bn.

samsonlawal

Podrias explicar cómo resolver Lim(1/(3^n))=0

Newsoftheworldactually

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